In this paper, we compare two regression curves by measuring their difference by the area between the two curves, represented by their L1 -distance. We develop asymptotic confidence intervals for this measure and statistical tests to investigate the similarity/equivalence of the two curves. Bootstrap methodology specifically designed for equivalence testing is developed to obtain procedures with good finite sample properties and its consistency is rigorously proved. The finite sample properties are investigated by means of a small simulation study. © 2023, The Institute of Statistical Mathematics, Tokyo.

We propose a reproducing kernel Hilbert space approach for statistical inference regarding the slope in a function-on-function linear regression via penalised least squares, regularized by the thin-plate spline smoothness penalty. We derive a Bahadur expansion for the slope surface estimator and prove its weak convergence as a process in the space of all continuous functions. As a consequence of these results, we construct minimax optimal estimates, simultaneous confidence regions for the slope surface and simultaneous prediction bands. Moreover, we derive new tests for the hypothesis that the maximum deviation between the “true” slope surface and a given surface is less than or equal to a given threshold. In other words, we are not trying to test for exact equality (because in many applications this hypothesis is hard to justify), but rather for pre-specified deviations under the null hypothesis. To ensure practicability, non-standard bootstrap procedures are developed addressing particular features that arise in these testing problems. We also demonstrate that the new methods have good finite sample properties by means of a simulation study and illustrate their practicability by analyzing a data example. © 2024 ISI/BS.

In this paper we develop a novel bootstrap test for the comparison of two multinomial distributions. The two distributions are called equivalent or similar if a norm of the difference between the class probabilities is smaller than a given threshold. In contrast to most of the literature our approach does not require differentiability of the norm and is in particular applicable for the maximum- and L1-norm. © 2023 Elsevier B.V.

There is a typographic error in the title of the manuscript (“lower urinary tract systems” instead of “lower urinary tract symptoms”). The correct title is as follows: Data Mining in Urology: Understanding Real-world Treatment Pathways for Lower Urinary Tract Symptoms via Exploration of Big Data Conflicts of interest: Christian Gratzke has received grants/research support from Astellas Pharma, Bayer, GSK, MSD, and Recordati, and honoraria or consultation fees from Amgen, Astellas Pharma, Bayer, GSK, Ipsen, Janssen, Lilly Pharma, Recordati, Pfizer, Rottapharm, and Steba Biotech. Arkadiusz Miernik has received research funding from the German Federal Ministry of Education and Research; has received travel expenses from the German Association of Urology and the European Association of Urology; is an advisor for KLS Martin, Dornier MedTech Europe, Richard Wolf, Karl Storz, Lisa Laser Products, Boston Scientific, Medi-Tate, and B. Braun New Ventures; is a reviewer for Ludwig Boltzmann Gesellschaft; and has received royalties from Walter de Gruyter and Springer Science + Business Media. The remaining authors have nothing to disclose. © 2022 European Association of Urology

For a spatiotemporal process (Figure presented.), where (Figure presented.) denotes the set of spatial locations and (Figure presented.) the time domain, we consider the problem of testing for a change in the sequence of mean functions (Figure presented.). In contrast to most of the literature, we are not interested in arbitrarily small changes but only in changes with a norm exceeding a given threshold. Asymptotically distribution free tests are proposed, which do not require the estimation of the long-run spatiotemporal covariance structure. In particular, we consider a fully functional approach and a test based on the cumulative sum paradigm, investigate the large sample properties of the corresponding test statistics and study their finite sample properties by means of simulation study. © 2022 The Authors. Journal of Time Series Analysis published by John Wiley & Sons Ltd.

We consider the problem of predicting values of a random process or field satisfying a linear model y(x) = θ⊤f(x) + ε(x) , where errors ε(x) are correlated. This is a common problem in kriging, where the case of discrete observations is standard. By focussing on the case of continuous observations, we derive expressions for the best linear unbiased predictors and their mean squared error. Our results are also applicable in the case where the derivatives of the process y are available, and either a response or one of its derivatives need to be predicted. The theoretical results are illustrated by several examples in particular for the popular Matérn 3/2 kernel. © 2023, The Author(s).

In this paper, we develop statistical inference tools for high-dimensional functional time series. We introduce a new concept of physical dependent processes in the space of square integrable functions, which adopts the idea of basis decomposition of functional data in these spaces, and derive Gaussian and multiplier bootstrap approximations for sums of high-dimensional functional time series. These results have numerous important statistical consequences. Exemplarily, we consider the development of joint simultaneous confidence bands for the mean functions and the construction of tests for the hypotheses that the mean functions in the panel dimension are parallel. The results are illustrated by means of a small simulation study and in the analysis of Canadian temperature data. © 2023 (RSS) Royal Statistical Society. All rights reserved.

We focus on estimating daily integrated volatility (IV) by realized measures based on intraday returns following a discrete-time stochastic model with a pronounced intraday periodicity (IP). We demonstrate that neglecting the IP-impact on realized estimators may lead to invalid statistical inference concerning IV for a common finite number of intraday returns. For a given IP functional form, we analytically derive robust IP-correction factors for realized measures of IV as well as their asymptotic distributions. We show both in Monte Carlo simulations and empirically that the proposed bias corrections are the robust way to account for IP by computing realized estimators. © 2022, The Author(s).

Many materials processes and properties depend on the anisotropy of the energy of grain boundaries, i.e. on the fact that this energy is a function of the five geometric degrees of freedom (DOF) of the interface. To access this parameter space in an efficient way and to discover energy cusps in unexplored regions, a method was recently established, which combines atomistic simulations with statistical methods (Kroll et al., 2022). This sequential sampling technique is now extended in the spirit of an active learning algorithm by adding a criterion to decide when the sampling has advanced enough to stop. In this instance, two parameters to analyse the sampling results on the fly are introduced: the number of cusps, which correspond to the most interesting and important regions of the energy landscape, and the maximum change of energy between two sequential iterations. Monitoring these two quantities provides valuable insight into how the subspaces are energetically structured. The combination of both parameters provides the necessary information to evaluate the sampling of the 2D subspaces of grain boundary plane inclinations of even non-periodic, low angle grain boundaries. With a reasonable number of data points in the initial design, only a few appropriately chosen sequential iterations already improve the accuracy of the sampling substantially and unknown cusps can be found within a few additional sequential steps. © 2023 The Author(s)

This study examines two-sample tests for functional time series data, which have become widely available with the advent of modern complex observation systems. Here, we evaluate whether two sets of functional time series observations share the shape of their primary modes of variation, as encoded by the eigenfunctions of the respective covariance operators. To this end, a novel testing approach is introduced that adds to existing literature in two main ways. First, tests are set up in the relevant testing framework, where interest is not in testing an exact null hypothesis, but rather in detecting deviations deemed sufficiently relevant, with relevance determined by the practitioner and perhaps guided by domain experts. Second, the proposed test statistics rely on a self-normalization principle that helps to avoid the notoriously difficult task of estimating the long-run covariance structure of the underlying functional time series. The main theoretical result of this study is the derivation of the large-sample behavior of the proposed test statistics. Empirical evidence, which indicates that the proposed procedures work well in finite samples and compare favorably with competing methods, is provided through a simulation study and an application to annual temperature data. © 2023 Institute of Statistical Science. All rights reserved.

The classical approach to analyze pharmacokinetic (PK) data in bioequivalence studies aiming to compare two different formulations is to perform noncompartmental analysis (NCA) followed by two one-sided tests (TOST). In this regard, the PK parameters area under the curve (AUC) and $C_{\max}$ are obtained for both treatment groups and their geometric mean ratios are considered. According to current guidelines by the U.S. Food and Drug Administration and the European Medicines Agency, the formulations are declared to be sufficiently similar if the $90\%$ confidence interval for these ratios falls between $0.8$ and $1.25 $. As NCA is not a reliable approach in case of sparse designs, a model-based alternative has already been proposed for the estimation of $\rm AUC$ and $C_{\max}$ using nonlinear mixed effects models. Here we propose another, more powerful test than the TOST and demonstrate its superiority through a simulation study both for NCA and model-based approaches. For products with high variability on PK parameters, this method appears to have closer type I errors to the conventionally accepted significance level of $0.05$, suggesting its potential use in situations where conventional bioequivalence analysis is not applicable. © The Author 2020. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

In the common time series model Xi,n = μ(i/n) +εi,n with non-stationary errors we consider the problem of detecting a significant deviation of the mean function μ from a benchmark g(μ) (suchastheini-tial value μ(0) or the average trend∫ 1 0 μ(t)dt). The problem is motivated by a more realistic modelling of change point analysis, where one is inter-ested in identifying relevant deviations in a smoothly varying sequence of means (μ(i/n))i=1,…,n and cannot assume that the sequence is piecewise constant. A test for this type of hypotheses is developed using an appro-priate estimator for the integrated squared deviation of the mean function and the threshold. By a new concept of self-normalization adapted to non-stationary processes an asymptotically pivotal test for the hypothesis of a relevant deviation is constructed. The results are illustrated by means of a simulation study and a data example. © 2021, Institute of Mathematical Statistics. All rights reserved.

We propose a new sequential monitoring scheme for changes in the parameters of a multivariate time series. In contrast to procedures proposed in the literature which compare an estimator from the training sample with an estimator calculated from the remaining data, we suggest to divide the sample at each time point after the training sample. Estimators from the sample before and after all separation points are then continuously compared calculating a maximum of norms of their differences. For open-end scenarios our approach yields an asymptotic level (Formula presented.) procedure, which is consistent under the alternative of a change in the parameter. By means of a simulation study it is demonstrated that the new method outperforms the commonly used procedures with respect to power and the feasibility of our approach is illustrated by analyzing two data examples. © 2020 The Authors. Journal of Time Series Analysis published by John Wiley & Sons Ltd.

We propose a new measure for stationarity in functional time series that is based on an explicit representation of the L2-distance between the spectral density operator of a nonstationary process and its best (L2-)approximation by a spectral density operator corresponding to a stationary process. This distance can be estimated by the sum of the Hilbert-Schmidt inner products of the periodogram operators (evaluated at different frequencies). Furthermore, the asymptotic normality of an appropriately standardized version of the estimator can be established for the corresponding estimator under the null and alternative hypotheses. As a result, we obtain a simple asymptotic frequency-domain level α-test (using the quantiles of the normal distribution) to test for the hypothesis of stationarity of a functional time series. We also briefly discuss other applications, such as asymptotic confidence intervals for the measure of stationarity, or the construction of tests for “relevant deviations from stationarity”. We demonstrate in a small simulation study that the new method has very good finite-sample properties. Moreover, we apply our test to annual temperature curves. © 2021 Institute of Statistical Science. All rights reserved.

In this note we consider the optimal design problem for estimating the slope of a polynomial regression with no intercept at a given point, say z. In contrast to previous work, we investigate the model on the non-symmetric interval. © 2020 Elsevier B.V.

Due to the surge of data storage techniques, the need for the development of appropriate techniques to identify patterns and to extract knowledge from the resulting enormous data sets, which can be viewed as collections of dependent functional data, is of increasing interest in many scientific areas. We develop a similarity measure for spectral density operators of a collection of functional time series, which is based on the aggregation of Hilbert–Schmidt differences of the individual time-varying spectral density operators. Under fairly general conditions, the asymptotic properties of the corresponding estimator are derived and asymptotic normality is established. The introduced statistic lends itself naturally to quantify (dis)-similarity between functional time series, which we subsequently exploit in order to build a spectral clustering algorithm. Our algorithm is the first of its kind in the analysis of non-stationary (functional) time series and enables to discover particular patterns by grouping together ‘similar’ series into clusters, thereby reducing the complexity of the analysis considerably. The algorithm is simple to implement and computationally feasible. As a further application, we provide a simple test for the hypothesis that the second order properties of two non-stationary functional time series coincide. © 2021 ISI/BS.

Classical change point analysis aims at (1) detecting abrupt changes in the mean of a possibly nonstationary time series and at (2) identifying regions where the mean exhibits a piecewise constant behavior. In many applications however, it is more reasonable to assume that the mean changes gradually in a smooth way. Those gradual changes may either be nonrelevant (i.e., small), or relevant for a specific problem at hand, and the present paper presents statistical methodology to detect the latter. More precisely, we consider the common nonparametric regression model Xi = μ(i/n) + εi with centered errors and propose a test for the null hypothesis that the maximum absolute deviation of the regression function μ from a functional g(μ) (such as the value μ(0) or the integral 01 μ(t)dt) is smaller than a given threshold on a given interval [x0, x1] ⊆ [0, 1]. A test for this type of hypotheses is developed using an appropriate estimator, say d∞,n, for the maximum deviation d∞ = supt∈[x0,x1] |μ(t) − g(μ)|. We derive the limiting distribution of an appropriately standardized version of d∞,n, where the standardization depends on the Lebesgue measure of the set of extremal points of the function μ(·) − g(μ). A refined procedure based on an estimate of this set is developed and its consistency is proved. The results are illustrated by means of a simulation study and a data example. © Institute of Mathematical Statistics, 2021

Diurnal fluctuations in volatility are a well-documented stylized fact of intraday price data. This warrants an investigation how this intraday periodicity (IP) affects both finite sample as well as asymptotic properties of several popular realized estimators of daily integrated volatility which are based on functionals of a finite number of intraday returns. It turns out that most of the estimators considered in this study exhibit a finite-sample bias due to IP, which can however get negligible when the number of intraday returns diverges to infinity. The appropriate correction factors for this bias are derived based on estimates of the IP. The adequacy of the new corrections is evaluated by means of a Monte Carlo simulation study and an empirical example. © 2021 EcoSta Econometrics and Statistics

In this paper we propose statistical inference tools for the covariance operators of functional time series in the two sample and change point problem. In contrast to most of the literature, the focus of our approach is not testing the null hypothesis of exact equality of the covariance operators. Instead, we propose to formulate the null hypotheses in the form that “the distance between the operators is small”, where we measure deviations by the sup-norm. We provide powerful bootstrap tests for these type of hypotheses, investigate their asymptotic properties and study their finite sample properties by means of a simulation study. © 2021, The Institute of Statistical Mathematics, Tokyo.

Detecting structural changes in functional data is a prominent topic in statistical literature. However not all trends in the data are important in applications, but only those of large enough influence. In this paper we address the problem of identifying relevant changes in the eigenfunctions and eigenvalues of covariance kernels of L2[0, 1]-valued time series. By selfnormalization techniques we derive pivotal, asymptotically consistent tests for relevant changes in these characteristics of the second order structure and investigate their finite sample properties in a simulation study. The applicability of our approach is demonstrated analyzing German annual temperature data. © 2021, Institute of Mathematical Statistics. All rights reserved.

This article studies the problem whether two convex (concave) regression functions modelling the relation between a response and covariate in two samples differ by a shift in the horizontal and/or vertical axis. We consider a nonparametric situation assuming only smoothness of the regression functions. A graphical tool based on the derivatives of the regression functions and their inverses is proposed to answer this question and studied in several examples. We also formalize this question in a corresponding hypothesis and develop a statistical test. The asymptotic properties of the corresponding test statistic are investigated under the null hypothesis and local alternatives. In contrast to most of the literature on comparing shape invariant models, which requires independent data the procedure is applicable for dependent and non-stationary data. We also illustrate the finite sample properties of the new test by means of a small simulation study and two real data examples. © 2021, The Institute of Statistical Mathematics, Tokyo.

We consider the problem of designing experiments for the comparison of two regression curves describing the relation between a predictor and a response in two groups, where the data between and within the group may be dependent. In order to derive efficient designs we use results from stochastic analysis to identify the best linear unbiased estimator (BLUE) in a corresponding continuous model. It is demonstrated that in general simultaneous estimation using the data from both groups yields more precise results than estimation of the parameters separately in the two groups. Using the BLUE from simultaneous estimation, we then construct an efficient linear estimator for finite sample size by minimizing the mean squared error between the optimal solution in the continuous model and its discrete approximation with respect to the weights (of the linear estimator). Finally, the optimal design points are determined by minimizing the maximal width of a simultaneous confidence band for the difference of the two regression functions. The advantages of the new approach are illustrated by means of a simulation study, where it is shown that the use of the optimal designs yields substantially narrower confidence bands than the application of uniform designs. © 2021, The Author(s).

In this paper we construct optimal designs for frequentist model averaging estimation. We derive the asymptotic distribution of the model averaging estimate with fixed weights in the case where the competing models are non-nested. A Bayesian optimal design minimizes an expectation of the asymptotic mean squared error of the model averaging estimate calculated with respect to a suitable prior distribution. We derive a necessary condition for the optimality of a given design with respect to this new criterion. We demonstrate that Bayesian optimal designs can improve the accuracy of model averaging substantially. Moreover, the derived designs also improve the accuracy of estimation in a model selected by model selection and model averaging estimates with random weights. © 2021, The Author(s).

We investigate the problem of designing experiments for series estimators in nonparametric regression models with correlated observations. We use projection-based estimators to derive an explicit solution of the best linear oracle estimator in the continuous-time model for all Markovian-type error processes. These solutions are then used to construct estimators, which can be calculated from the available data, along with their corresponding optimal design points. Our results are illustrated by means of a simulation study, which demonstrates that the proposed series estimator outperforms commonly used techniques based on the optimal linear unbiased estimators. Moreover, we show that the performance of the proposed estimators can be further improved by choosing the design points appropriately. © 2021 Institute of Statistical Science. All rights reserved.

Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor wants to realize the position suggested by the optimal portfolios, he/she needs to estimate the unknown parameters and to account for the parameter uncertainty in the decision process. Most often, the parameters of interest are the population mean vector and the population covariance matrix of the asset return distribution. In this paper, we characterize the exact sampling distribution of the estimated optimal portfolio weights and their characteristics. This is done by deriving their sampling distribution by its stochastic representation. This approach possesses several advantages, e.g. (i) it determines the sampling distribution of the estimated optimal portfolio weights by expressions, which could be used to draw samples from this distribution efficiently; (ii) the application of the derived stochastic representation provides an easy way to obtain the asymptotic approximation of the sampling distribution. The later property is used to show that the high-dimensional asymptotic distribution of optimal portfolio weights is a multivariate normal and to determine its parameters. Moreover, a consistent estimator of optimal portfolio weights and their characteristics is derived under the high-dimensional settings. Via an extensive simulation study, we investigate the finite-sample performance of the derived asymptotic approximation and study its robustness to the violation of the model assumptions used in the derivation of the theoretical results. © 2022 World Scientific Publishing Company.

In this article, we propose a new approach for sequential monitoring of a general class of parameters of a d-dimensional time series, which can be estimated by approximately linear functionals of the empirical distribution function. We consider a closed-end method, which is motivated by the likelihood ratio test principle and compare the new method with two alternative procedures. We also incorporate self-normalization such that estimation of the long-run variance is not necessary. We prove that for a large class of testing problems the new detection scheme has asymptotic level α and is consistent. The asymptotic theory is illustrated for the important cases of monitoring a change in the mean, variance, and correlation. By means of a simulation study it is demonstrated that the new test performs better than the currently available procedures for these problems. Finally, the methodology is illustrated by a small data example investigating index prices from the dot-com bubble. Supplementary materials for this article are available online. © 2019 American Statistical Association.

The assumption of separability is a simplifying and very popular assumption in the analysis of spatiotemporal or hypersurface data structures. It is often made in situations where the covariance structure cannot be easily estimated, for example, because of a small sample size or because of computational storage problems. In this paper we propose a new and very simple test to validate this assumption. Our approach is based on a measure of separability which is zero in the case of separability and positive otherwise. We derive the asymptotic distribution of a corresponding estimate under the null hypothesis and the alternative and develop an asymptotic and a bootstrap test which are very easy to implement. In particular, our approach does neither require projections on subspaces generated by the eigenfunctions of the covariance operator nor distributional assumptions as recently used by (Ann. Statist. 45 (2017) 1431–1461) and (Biometrika 104 425–437) to construct tests for separability. We investigate the finite sample performance by means of a simulation study and also provide a comparison with the currently available methodology. Finally, the new procedure is illustrated analyzing a data example. © Institute of Mathematical Statistics, 2020.

A time-domain test for the assumption of second-order stationarity of a functional time series is proposed. The test is based on combining individual cumulative sum tests which are designed to be sensitive to changes in the mean, variance and autocovariance operators, respectively. The combination of their dependent p values relies on a joint-dependent block multiplier bootstrap of the individual test statistics. Conditions under which the proposed combined testing procedure is asymptotically valid under stationarity are provided. A procedure is proposed to automatically choose the block length parameter needed for the construction of the bootstrap. The finite-sample behavior of the proposed test is investigated in Monte Carlo experiments, and an illustration on a real data set is provided. © 2019, The Institute of Statistical Mathematics, Tokyo.

In clinical trials, the comparison of two different populations is a common problem. Nonlinear (parametric) regression models are commonly used to describe the relationship between covariates, such as concentration or dose, and a response variable in the two groups. In some situations, it is reasonable to assume some model parameters to be the same, for instance, the placebo effect or the maximum treatment effect. In this paper, we develop a (parametric) bootstrap test to establish the similarity of two regression curves sharing some common parameters. We show by theoretical arguments and by means of a simulation study that the new test controls its significance level and achieves a reasonable power. Moreover, it is demonstrated that under the assumption of common parameters, a considerably more powerful test can be constructed compared with the test that does not use this assumption. Finally, we illustrate the potential applications of the new methodology by a clinical trial example. © 2019 The Authors. Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society

This article considers the problem of estimating a change point in the covariance matrix in a sequence of high-dimensional vectors, where the dimension is substantially larger than the sample size. A two-stage approach is proposed to efficiently estimate the location of the change point. The first step consists of a reduction of the dimension to identify elements of the covariance matrices corresponding to significant changes. In a second step, we use the components after dimension reduction to determine the position of the change point. Theoretical properties are developed for both steps, and numerical studies are conducted to support the new methodology. Supplementary materials for this article are available online. © 2020 American Statistical Association.

Functional data analysis is typically conducted within the L2-Hilbert space framework. There is by now a fully developed statistical toolbox allowing for the principled application of the functional data machinery to real-world problems, often based on dimension reduction techniques such as functional principal component analysis. At the same time, there have recently been a number of publications that sidestep dimension reduction steps and focus on a fully functional L2-methodology. This paper goes one step further and develops data analysis methodology for functional time series in the space of all continuous functions. The work is motivated by the fact that objects with rather different shapes may still have a small L2-distance and are therefore identified as similar when using a L2-metric. However, in applications it is often desirable to use metrics reflecting the visualization of the curves in the statistical analysis. The methodological contributions are focused on developing two-sample and change-point tests as well as confidence bands, as these procedures appear to be conducive to the proposed setting. Particular interest is put on relevant differences; that is, on not trying to test for exact equality, but rather for prespecified deviations under the null hypothesis. The procedures are justified through large-sample theory. To ensure practicability, nonstandard bootstrap procedures are developed and investigated addressing particular features that arise in the problem of testing relevant hypotheses. The finite sample properties are explored through a simulation study and an application to annual temperature profiles. © Institute of Mathematical Statistics, 2020

In this paper, we investigate the asymptotic distribution of likelihood ratio tests in models with several groups, when the number of groups converges with the dimension and sample size to infinity. We derive central limit theorems for the logarithm of various test statistics and compare our results with the approximations obtained from a central limit theorem where the number of groups is fixed. © 2020 Elsevier Inc.

In this article we study the theoretical properties of the simultaneous multiscale change point estimator (SMUCE) in piecewise-constant signal models with dependent error processes. Empirical studies suggest that in this case the change point estimate is inconsistent, but it is not known if alternatives suggested in the literature for correlated data are consistent. We propose a modification of SMUCE scaling the basic statistic by the long run variance of the error process, which is estimated by a difference-type variance estimator calculated from local means from different blocks. For this modification we prove model consistency for physical-dependent error processes and illustrate the finite sample performance by means of a simulation study. © 2020 Board of the Foundation of the Scandinavian Journal of Statistics

In traditional pharmacokinetic (PK) bioequivalence analysis, two one-sided tests (TOST) are conducted on the area under the concentration-time curve and the maximal concentration derived using a non-compartmental approach. When rich sampling is unfeasible, a model-based (MB) approach, using nonlinear mixed effect models (NLMEM) is possible. However, MB-TOST using asymptotic standard errors (SE) presents increased type I error when asymptotic conditions do not hold. In this work, we propose three alternative calculations of the SE based on (i) an adaptation to NLMEM of the correction proposed by Gallant, (ii) the a posteriori distribution of the treatment coefficient using the Hamiltonian Monte Carlo algorithm, and (iii) parametric random effects and residual errors bootstrap. We evaluate these approaches by simulations, for two-arms parallel and two-period, two-sequence cross-over design with rich (n = 10) and sparse (n = 3) sampling under the null and the alternative hypotheses, with MB-TOST. All new approaches correct for the inflation of MB-TOST type I error in PK studies with sparse designs. The approach based on the a posteriori distribution appears to be the best compromise between controlled type I errors and computing times. MB-TOST using non-asymptotic SE controls type I error rate better than when using asymptotic SE estimates for bioequivalence on PK studies with sparse sampling. © 2020, American Association of Pharmaceutical Scientists.

We identify optimal designs for estimating individual coefficients in a polynomial regression with no intercept. Here the regression functions do not form a Chebyshev system such that the seminal results of Studden (1968) characterizing c-optimal designs are not applicable. © 2019

We develop an estimator for the high-dimensional covariance matrix of a locally stationary process with a smoothly varying trend and use this statistic to derive consistent predictors in nonstationary time series. In contrast to the currently available methods for this problem the predictor developed here does not rely on fitting an autoregressive model and does not require a vanishing trend. The finite sample properties of the new methodology are illustrated by means of a simulation study and a financial indices study. Supplementary materials for this article are available online. © 2020 American Statistical Association.

Residual-based analysis is generally considered a cornerstone of statistical methodology. For a special case of indirect regression, we investigate a residual-based empirical distribution function and provide a uniform expansion of this estimator, which is also shown to be asymptotically most precise. This investigation naturally leads to a completely data-driven technique for selecting the regularization parameter used in our indirect regression function estimator. The resulting methodology is based on a smooth bootstrap of the model residuals. A simulation study demonstrates the effectiveness of our approach. © 2020 Institute of Statistical Science. All rights reserved.

We develop methodology for testing relevant hypotheses about functional time series in a tuning-free way. Instead of testing for exact equality, e.g. for the equality of two mean functions from two independent time series, we propose to test the null hypothesis of no relevant deviation. In the two-sample problem this means that an L2-distance between the two mean functions is smaller than a prespecified threshold. For such hypotheses self-normalization, which was introduced in 2010 by Shao, and Shao and Zhang and is commonly used to avoid the estimation of nuisance parameters, is not directly applicable. We develop new self-normalized procedures for testing relevant hypotheses in the one-sample, two-sample and change point problem and investigate their asymptotic properties. Finite sample properties of the tests proposed are illustrated by means of a simulation study and data examples. Our main focus is on functional time series, but extensions to other settings are also briefly discussed. © 2020 Royal Statistical Society

A restrictive assumption in change point analysis is “stationarity under the null hypothesis of no change-point”, which is crucial for asymptotic theory but not very realistic from a practical point of view. For example, if change point analysis for correlations is performed, it is not necessarily clear that the mean, marginal variance or higher order moments are constant, even if there is no change in the correlation. This paper develops change point analysis for the correlation structures under less restrictive assumptions. In contrast to previous work, our approach does not require that the mean, variance and fourth order joint cumulants are constant under the null hypothesis. Moreover, we also address the problem of detecting relevant change points. © 2019 Institute of Statistical Science. All rights reserved.

This paper considers the problem of testing if a sequence of means (μt )t=1,.,n of a nonstationary time series (Xt )t=1,.,n is stable in the sense that the difference of the means μ1 and μt between the initial time t = 1 and any other time is smaller than a given threshold, that is |μ1 - μt| ≤ c for all t = 1, . , n. A test for hypotheses of this type is developed using a bias corrected monotone rearranged local linear estimator and asymptotic normality of the corresponding test statistic is established. As the asymptotic variance depends on the location of the roots of the equation |μ1 - μt| = c a new bootstrap procedure is proposed to obtain critical values and its consistency is established. As a consequence we are able to quantitatively describe relevant deviations of a nonstationary sequence from its initial value. The results are illustrated by means of a simulation study and by analyzing data examples. © Institute of Mathematical Statistics, 2019.

We consider the moment space M2n+1 dn of moments up to the order 2n+1 of dn×dn real matrix measures defined on the interval [0,1]. The asymptotic properties of the Hankel determinant {logdet(Mi+jdn)i,j=0,…,⌊nt⌋}t∈[0,1] of a uniformly distributed vector (M1,…,M2n+1)t∼U(M2n+1) are studied when the dimension n of the moment space and the size of the matrices dn converge to infinity. In particular weak convergence of an appropriately centered and standardized version of this process is established. Mod-Gaussian convergence is shown and several large and moderate deviation principles are derived. Our results are based on some new relations between determinants of subblocks of the Jacobi-beta-ensemble, which are of their own interest and generalize Bartlett decomposition-type results for the Jacobi-beta-ensemble from the literature. © 2019 Elsevier B.V.

We propose a goodness-of-fit test for the distribution of errors from a multivariate indirect regression model, which we assume belongs to a location-scale family under the null hypothesis. The test statistic is based on the Khmaladze transformation of the empirical process of standardized residuals. This goodness-of-fit test is consistent at the root-n rate of convergence, and the test can maintain power against local alternatives converging to the null at a root-n rate. © 2019, Institute of Mathematical Statistics. All rights reserved.

This paper introduces test and estimation procedures for abrupt and gradual changes in the entire jump behaviour of a discretely observed Itō semimartingale. In contrast to existing work we analyse jumps of arbitrary size which are not restricted to a minimum height. Our methods are based on weak convergence of a truncated sequential empirical distribution function of the jump characteristic of the underlying Itō semimartingale. Critical values for the new tests are obtained by a multiplier bootstrap approach and we investigate the performance of the tests also under local alternatives. An extensive simulation study shows the finite-sample properties of the new procedures. © 2019, Institute of Mathematical Statistics. All rights reserved.

We consider the problem of designing experiments for estimating a target parameter in regression analysis when there is uncertainty about the parametric form of the regression function. A newoptimality criterion is proposed that chooses the experimental design to minimize the asymptotic mean squared error of the frequentist model averaging estimate. Necessary conditions for the optimal solution of a locally and Bayesian optimal design problem are established. The results are illustrated in several examples, and it is demonstrated that Bayesian optimal designs can yield a reduction of the mean squared error of the model averaging estimator by up to 45%. © 2019 Biometrika Trust.

In this paper optimal designs for regression problems with spherical predictors of arbitrary dimension are considered. Our work is motivated by applications in material sciences, where crystallographic textures such as the misorientation distribution or the grain boundary distribution (depending on a four dimensional spherical predictor) are represented by series of hyperspherical harmonics, which are estimated from experimental or simulated data. For this type of estimation problems we explicitly determine optimal designs with respect to the Φ p -criteria introduced by Kiefer (1974) and a class of orthogonally invariant information criteria recently introduced in the literature. In particular, we show that the uniform distribution on the m-dimensional sphere is optimal and construct discrete and implementable designs with the same information matrices as the continuous optimal designs. Finally, we illustrate the advantages of the new designs for series estimation by hyperspherical harmonics, which are symmetric with respect to the first and second crystallographic point group. © 2019, Institute of Mathematical Statistics. All rights reserved.

In this paper, we consider the optimal design problem for extrapolation and estimation of the slope at a given point, say z, in a polynomial regression with no intercept. We provide explicit solutions of these problems in many cases and characterize those values of z, where this is not possible. © 2019, The Institute of Statistical Mathematics, Tokyo.

In this paper, new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type statistics for the hypothesis of a block diagonal covariance matrix. The asymptotic properties of the new test statistics are investigated under the null hypothesis and the alternative hypothesis using random matrix theory. For this purpose, we study the weak convergence of linear spectral statistics of central and (conditionally) noncentral Fisher matrices. In particular, a central limit theorem for linear spectral statistics of large dimensional (conditionally) noncentral Fisher matrices is derived which is then used to analyse the power of the tests under the alternative. The theoretical results are illustrated by means of a simulation study where we also compare the new tests with several alternative, in particular with the commonly used corrected likelihood ratio test. It is demonstrated that the latter test does not keep its nominal level, if the dimension of one subvector is relatively small compared to the dimension of the other sub-vector. On the other hand, the tests proposed in this paper provide a reasonable approximation of the nominal level in such situations. Moreover, we observe that one of the proposed tests is most powerful under a variety of correlation scenarios. © Institute of Mathematical Statistics, 2019.

In this paper, the problem of best linear unbiased estimation is investigated for continuous-time regression models. We prove several general statements concerning the explicit form of the best linear unbiased estimator (BLUE), in particular when the error process is a smooth process with one or several derivatives of the response process available for construction of the estimators. We derive the explicit form of the BLUE for many specific models including the cases of continuous autoregressive errors of order two and integrated error processes (such as integrated Brownian motion). The results are illustrated on many examples. © 2019 Institute of Mathematical Statistics. © 2019 Institute of Mathematical Statistics. All rights reserved.

In this paper we investigate an indirect regression model characterized by the Radon transformation. This model is useful for recovery of medical images obtained by computed tomography scans. The indirect regression function is estimated using a series estimator motivated by a spectral cutoff technique. Further, we investigate the empirical process of residuals from this regression, and show that it satisfies a functional central limit theorem. © 2019, Allerton Press, Inc.

In contrast to conventional model selection criteria, the Focused Information Criterion (FIC) allows for the purpose-specific choice of model specifications. This accommodates the idea that one kind of model might be highly appropriate for inferences on a particular focus parameter, but not for another. Using the FIC concept that is developed by Behl, Claeskens, and Dette (2014) for quantile regression analysis, and the estimation of the rebound effect in individual mobility behavior as an example, this paper provides for an empirical application of the FIC in the selection of quantile regression models. © 2018 Board of Trustees of the University of Illinois

We propose a new procedure for white noise testing of a functional time series. Our approach is based on an explicit representation of the L2-distance between the spectral density operator and its best (L2-)approximation by a spectral density operator corresponding to a white noise process. The estimation of this distance can be easily accomplished by sums of periodogram kernels, and it is shown that an appropriately standardized version of the estimator is asymptotically normal distributed under the null hypothesis (of functional white noise) and under the alternative. As a consequence, we obtain a very simple test (using the quantiles of the normal distribution) for the hypothesis of a white noise functional process. In particular, the test does not require either the estimation of a long-run variance (including a fourth order cumulant) or resampling procedures to calculate critical values. Moreover, in contrast to all other methods proposed in the literature, our approach also allows testing for ‘relevant’ deviations from white noise and constructing confidence intervals for a measure that measures the discrepancy of the underlying process from a functional white noise process. Copyright © 2017 John Wiley & Sons Ltd

We consider 2 problems of increasing importance in clinical dose finding studies. First, we assess the similarity of 2 non-linear regression models for 2 non-overlapping subgroups of patients over a restricted covariate space. To this end, we derive a confidence interval for the maximum difference between the 2 given models. If this confidence interval excludes the pre-specified equivalence margin, similarity of dose response can be claimed. Second, we address the problem of demonstrating the similarity of 2 target doses for 2 non-overlapping subgroups, using again an approach based on a confidence interval. We illustrate the proposed methods with a real case study and investigate their operating characteristics (coverage probabilities, Type I error rates, power) via simulation. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper we consider the problem of detecting a change in the parameters of an autoregressive process where the moments of the innovation process do not necessarily exist. An empirical likelihood ratio test for the existence of a change point is proposed and its asymptotic properties are studied. In contrast to other works on change-point tests using empirical likelihood, we do not assume knowledge of the location of the change point. In particular, we prove that the maximizer of the empirical likelihood is a consistent estimator for the parameters of the autoregressive model in the case of no change point and derive the limiting distribution of the corresponding test statistic under the null hypothesis. We also establish consistency of the new test. A nice feature of the method is the fact that the resulting test is asymptotically distribution-free and does not require an estimate of the long-run variance. The asymptotic properties of the test are investigated by means of a small simulation study, which demonstrates good finite-sample properties of the proposed method. Copyright © 2018 John Wiley & Sons Ltd

This article investigates the problem whether the difference between two parametric models m1, m2 describing the relation between a response variable and several covariates in two different groups is practically irrelevant, such that inference can be performed on the basis of the pooled sample. Statistical methodology is developed to test the hypotheses H0: d(m1, m2) ⩾ ϵ versus H1: d(m1, m2) < ϵ to demonstrate equivalence between the two regression curves m1, m2 for a prespecified threshold ϵ, where d denotes a distance measuring the distance between m1 and m2. Our approach is based on the asymptotic properties of a suitable estimator (Formula presented.) of this distance. To improve the approximation of the nominal level for small sample sizes, a bootstrap test is developed, which addresses the specific form of the interval hypotheses. In particular, data have to be generated under the null hypothesis, which implicitly defines a manifold for the parameter vector. The results are illustrated by means of a simulation study and a data example. It is demonstrated that the new methods substantially improve currently available approaches with respect to power and approximation of the nominal level. © 2018 American Statistical Association

Classical spectral analysis is based on the discrete Fourier transform of the autocovariances. In this article we investigate the asymptotic properties of new frequency-domain methods where the autocovariances in the spectral density are replaced by alternative dependence measures that can be estimated by U-statistics. An interesting example is given by Kendall's τ, for which the limiting variance exhibits a surprising behavior. Copyright © 2017 John Wiley & Sons Ltd

Background: IDeAl (Integrated designs and analysis of small population clinical trials) is an EU funded project developing new statistical design and analysis methodologies for clinical trials in small population groups. Here we provide an overview of IDeAl findings and give recommendations to applied researchers. Method: The description of the findings is broken down by the nine scientific IDeAl work packages and summarizes results from the project's more than 60 publications to date in peer reviewed journals. In addition, we applied text mining to evaluate the publications and the IDeAl work packages' output in relation to the design and analysis terms derived from in the IRDiRC task force report on small population clinical trials. Results: The results are summarized, describing the developments from an applied viewpoint. The main result presented here are 33 practical recommendations drawn from the work, giving researchers a comprehensive guidance to the improved methodology. In particular, the findings will help design and analyse efficient clinical trials in rare diseases with limited number of patients available. We developed a network representation relating the hot topics developed by the IRDiRC task force on small population clinical trials to IDeAl's work as well as relating important methodologies by IDeAl's definition necessary to consider in design and analysis of small-population clinical trials. These network representation establish a new perspective on design and analysis of small-population clinical trials. Conclusion: IDeAl has provided a huge number of options to refine the statistical methodology for small-population clinical trials from various perspectives. A total of 33 recommendations developed and related to the work packages help the researcher to design small population clinical trial. The route to improvements is displayed in IDeAl-network representing important statistical methodological skills necessary to design and analysis of small-population clinical trials. The methods are ready for use. © 2018 The Author(s).

In applications the properties of a stochastic feature often change gradually rather than abruptly, that is: after a constant phase for some time they slowly start to vary. In this paper we discuss statistical inference for the detection and the localization of gradual changes in the jump characteristic of a discretely observed Ito semimartingale. We propose a new measure of time variation for the jump behaviour of the process. The statistical uncertainty of a corresponding estimate is analysed by deriving new results on the weak convergence of a sequential empirical tail integral process and a corresponding multiplier bootstrap procedure. © 2018 Elsevier B.V.

The uniqueness of the time-varying copula-based spectrum recently proposed by the authors is established via an asymptotic representation result involving Wigner–Ville spectra. Copyright © 2017 John Wiley & Sons Ltd

In this paper, we present a new method for determining optimal designs for enzyme inhibition kinetic models, which are used to model the influence of the concentration of a substrate and an inhibition on the velocity of a reaction. The approach uses a nonlinear transformation of the vector of predictors such that the model in the new coordinates is given by an incomplete response surface model. Although there exist no explicit solutions of the optimal design problem for incomplete response surface models so far, the corresponding design problem in the new coordinates is substantially more transparent, such that explicit or numerical solutions can be determined more easily. The designs for the original problem can finally be found by an inverse transformation of the optimal designs determined for the response surface model. We illustrate the method determining explicit solutions for the D-optimal design and for the optimal design problem for estimating the individual coefficients in a non-competitive enzyme inhibition kinetic model. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.

Much work on optimal discrimination designs assumes that the models of interest are fully specified, apart from unknown parameters. Recent work allows errors in the models to be nonnormally distributed but still requires the specification of the mean structures.Otsu (2008) proposed optimal discriminating designs for semiparametric models by generalizing the Kullback-Leibler optimality criterion proposed byLópez-Fidalgo et al. (2007). This paper develops a relatively simple strategy for finding an optimal discrimination design. We also formulate equivalence theorems to confirm optimality of a design and derive relations between optimal designs found here for discriminating semiparametric models and those commonly used in optimal discrimination design problems. © 2017 Biometrika Trust.

In drug development, comparability of dissolution profiles of 2 different formulations is usually assessed using the similarity factor f2. In practice, the drug dissolution profiles are deemed similar if the f2 exceeds 50, which occurs when a 10% maximum difference in the mean percentage of the dissolved drug at each time point between test and reference formulation is obtained. According to the Guideline on the Investigation of Bioequivalence (CPMP/EWP/QWP/1401/98 Rev. 1/ Corr **) use of the f2 is however restricted by a set of validity conditions. If some of these conditions are not satisfied, the f2 is not considered suitable, and alternative statistical methods are needed. In this article, we propose an inferential framework based on the maximum deviation between curves to test the comparability of drug dissolution profiles. The new methodology is applicable regardless whether the validity criteria of the f2 are met or not. Contrary to the f2, this approach also integrates the variability of the measurements over time and not only their average. To benchmark our method, we performed simulations informed by 3 real case studies provided by the European Medicines Agency and extracted from dossiers submitted to the Centralised Procedure for Marketing Authorisation Application. In the scenarios of the simulation study, the new method controlled its type I error rate when the maximum deviation was greater than the similarity acceptance limit of 10%. The power exceeded 80% for small values of the maximum deviation, while the test was more conservative for intermediate ones. Our results were also very robust to sampling variations. Based on these positive findings, we encourage applicants to consider the new maximum deviation–based method as a valid alternative to the f2, especially when the validity criteria of the latter are not met. Copyright © 2018 John Wiley & Sons, Ltd.

This paper investigates the problem of detecting relevant change points in the mean vector, say μt=(μ1,t,…,μd,t)T of a high dimensional time series (Zt)t∈Z. While the recent literature on testing for change points in this context considers hypotheses for the equality of the means μ(1) h and μ(2) h before and after the change points in the different components, we are interested in a null hypothesis of the form H0:|μ(1) h−μ(2) h|≤Δh for all h=1,…,d where Δ1,…,Δd are given thresholds for which a smaller difference of the means in the h-th component is considered to be non-relevant. This formulation of the testing problem is motivated by the fact that in many applications a modification of the statistical analysis might not be necessary, if the differences between the parameters before and after the change points in the individual components are small. This problem is of particular relevance in high dimensional change point analysis, where a small change in only one component can yield a rejection by the classical procedure although all components change only in a non-relevant way. We propose a new test for this problem based on the maximum of squared and integrated CUSUM statistics and investigate its properties as the sample size n and the dimension d both converge to infinity. In particular, using Gaussian approximations for the maximum of a large number of dependent random variables, we show that on certain points of the boundary of the null hypothesis a standardized version of the maximum converges weakly to a Gumbel distribution. This result is used to construct a consistent asymptotic level α test and a multiplier bootstrap procedure is proposed, which improves the finite sample performance of the test. The finite sample properties of the test are investigated by means of a simulation study and we also illustrate the new approach investigating data from hydrology. © 2018, Institute of Mathematical Statistics. All rights reserved.

This paper discusses the properties of certain risk estimators that recently regained popularity for choosing regularization parameters in ill-posed problems, in particular for sparsity regularization. They apply Stein’s unbiased risk estimator (SURE) to estimate the risk in either the space of the unknown variables or in the data space. We will call the latter PSURE in order to distinguish the two different risk functions. It seems intuitive that SURE is more appropriate for ill-posed problems, since the properties in the data space do not tell much about the quality of the reconstruction. We provide theoretical studies of both approaches for linear Tikhonov regularization in a finite dimensional setting and estimate the quality of the risk estimators, which also leads to asymptotic convergence results as the dimension of the problem tends to infinity. Unlike previous works which studied single realizations of image processing problems with a very low degree of ill-posedness, we are interested in the statistical behaviour of the risk estimators for increasing ill-posedness. Interestingly, our theoretical results indicate that the quality of the SURE risk can deteriorate asymptotically for ill-posed problems, which is confirmed by an extensive numerical study. The latter shows that in many cases the SURE estimator leads to extremely small regularization parameters, which obviously cannot stabilize the reconstruction. Similar but less severe issues with respect to robustness also appear for the PSURE estimator, which in comparison to the rather conservative discrepancy principle leads to the conclusion that regularization parameter choice based on unbiased risk estimation is not a reliable procedure for ill-posed problems. A similar numerical study for sparsity regularization demonstrates that the same issue appears in non-linear variational regularization approaches. © 2018 American Institute of Mathematical Sciences.

Let Mn(E) denote the set of vectors of the first n moments of probability measures on E⊂ℝ with existing moments. The investigation of such moment spaces in high dimension has found considerable interest in the recent literature. For instance, it has been shown that a uniformly distributed moment sequence in Mn([0,1]) converges in the large n limit to the moment sequence of the arcsine distribution. In this article we provide a unifying viewpoint by identifying classes of more general distributions on Mn(E) for E = [a; b]; E = ℝ+and E = ℝ, respectively, and discuss universality problems within these classes. In particular, we demonstrate that the moment sequence of the arcsine distribution is not universal for E being a compact interval. Rather, there is a universal family of moment sequences of which the arcsine moment sequence is one particular member. On the other hand, on the moment spaces Mn(ℝ+) and Mn(ℝ) the random moment sequences governed by our distributions exhibit for n → ∞ a universal behaviour: The first k moments of such a random vector converge almost surely to the first k moments of the Marchenko-Pastur distribution (half line) and Wigner’s semi-circle distribution (real line). Moreover, the fluctuations around the limit sequences are Gaussian. We also obtain moderate and large deviations principles and discuss relations of our findings with free probability. © 2018, University of Washington. All rights reserved.

This paper presents a new and efficient method for the construction of optimal designs for regression models with dependent error processes. In contrast to most of the work in this field, which starts with a model for a finite number of observations and considers the asymptotic properties of estimators and designs as the sample size converges to infinity, our approach is based on a continuous time model. We use results from stochastic analysis to identify the best linear unbiased estimator (BLUE) in this model. Based on the BLUE, we construct an efficient linear estimator and corresponding optimal designs in the model for finite sample size by minimizing the mean squared error between the optimal solution in the continuous time model and its discrete approximation with respect to the weights (of the linear estimator) and the optimal design points, in particular in the multiparameter case. In contrast to previous work on the subject, the resulting estimators and corresponding optimal designs are very efficient and easy to implement. This means that they are practically not distinguishable from the weighted least squares estimator and the corresponding optimal designs, which have to be found numerically by nonconvex discrete optimization. The advantages of the new approach are illustrated in several numerical examples. © 2017 Institute of Mathematical Statistics.

We find optimal designs for linear models using a novel algorithm that iteratively combines a semidefinite programming (SDP) approach with adaptive grid techniques. The proposed algorithm is also adapted to find locally optimal designs for nonlinear models. The search space is first discretized, and SDP is applied to find the optimal design based on the initial grid. The points in the next grid set are points that maximize the dispersion function of the SDP-generated optimal design using nonlinear programming. The procedure is repeated until a user-specified stopping rule is reached. The proposed algorithm is broadly applicable, and we demonstrate its flexibility using (i) models with one or more variables and (ii) differentiable design criteria, such as A-, D-optimality, and non-differentiable criterion like E-optimality, including the mathematically more challenging case when the minimum eigenvalue of the information matrix of the optimal design has geometric multiplicity larger than 1. Our algorithm is computationally efficient because it is based on mathematical programming tools and so optimality is assured at each stage; it also exploits the convexity of the problems whenever possible. Using several linear and nonlinear models with one or more factors, we show the proposed algorithm can efficiently find optimal designs. © 2017 Springer Science+Business Media New York

Bayesian optimality criteria provide a robust design strategy to parameter misspecification. We develop an approximate design theory for Bayesian D-optimality for nonlinear regression models with covariates subject to measurement errors. Both maximum likelihood and least squares estimation are studied, and explicit characterisations of the Bayesian D-optimal saturated designs for the Michaelis-Menten, Emax and exponential regression models are provided. Several data examples are considered for the case of no preference for specific parameter values, where Bayesian D-optimal saturated designs are calculated using the uniform prior and compared with several other designs, including the corresponding locally D-optimal designs, which are often used in practice. © 2017 John Wiley & Sons, Ltd.

We focus on the construction of confidence corridors for multivariate nonparametric generalized quantile regression functions. This construction is based on asymptotic results for the maximal deviation between a suitable nonparametric estimator and the true function of interest, which follow after a series of approximation steps including a Bahadur representation, a new strong approximation theorem, and exponential tail inequalities for Gaussian random fields. As a byproduct we also obtain multivariate confidence corridors for the regression function in the classical mean regression. To deal with the problem of slowly decreasing error in coverage probability of the asymptotic confidence corridors, which results in meager coverage for small sample sizes, a simple bootstrap procedure is designed based on the leading term of the Bahadur representation. The finite-sample properties of both procedures are investigated by means of a simulation study and it is demonstrated that the bootstrap procedure considerably outperforms the asymptotic bands in terms of coverage accuracy. Finally, the bootstrap confidence corridors are used to study the efficacy of the National Supported Work Demonstration, which is a randomized employment enhancement program launched in the 1970s. This article has supplementary materials online. © 2017 American Statistical Association.

An efficient algorithm for the determination of Bayesian optimal discriminating designs for competing regression models is developed, where the main focus is on models with general distributional assumptions beyond the “classical” case of normally distributed homoscedastic errors. For this purpose, we consider a Bayesian version of the Kullback–Leibler (KL). Discretizing the prior distribution leads to local KL-optimal discriminating design problems for a large number of competing models. All currently available methods either require a large amount of computation time or fail to calculate the optimal discriminating design, because they can only deal efficiently with a few model comparisons. In this article, we develop a new algorithm for the determination of Bayesian optimal discriminating designs with respect to the Kullback–Leibler criterion. It is demonstrated that the new algorithm is able to calculate the optimal discriminating designs with reasonable accuracy and computational time in situations where all currently available procedures are either slow or fail. © 2017 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

In the framework of materials design there is the demand for extensive databases of specific materials properties. In this work we suggest an improved strategy for creating future databases, especially for extrinsic properties that depend on several material parameters. As an example we choose the energy of grain boundaries as a function of their geometric degrees of freedom. The construction of many existing databases of grain boundary energies in face-centred and body centred cubic metals relied on the a-priori knowledge of the location of important cusps and maxima in the five-dimensional energy landscape, and on an as-densely-as-possible sampling strategy. We introduce two methods to improve the current state of the art. Based on an existing energy model the location and number of the energy minima along which the hierarchical sampling takes place is predicted from existing data points without any a-priori knowledge, using a predictor function. Furthermore we show that in many cases it is more efficient to use a sequential sampling in a “design of experiment” scheme, rather than sampling all observations homogeneously in one batch. This sequential design exhibits a smaller error than the simultaneous one, and thus can provide the same accuracy with fewer data points. The new strategy should be particularly beneficial in the exploration of grain boundary energies in new alloys and/or non-cubic structures. © 2016 Acta Materialia Inc.

For (Formula presented.) let (Formula presented.) denote the Hankel matrix of order (Formula presented.) of a random vector (Formula presented.) on the moment space (Formula presented.) of all moments (up to the order 2n) of probability measures on the interval (Formula presented.). In this paper we study the asymptotic properties of the stochastic process (Formula presented.) as (Formula presented.). In particular weak convergence and corresponding large deviation principles are derived after appropriate standardization. © 2016 Springer Science+Business Media New York

In this paper, we propose methods for inference of the geometric features of a multivariate density. Our approach uses multiscale tests for the monotonicity of the density at arbitrary points in arbitrary directions. In particular, a significance test for a mode at a specific point is constructed. Moreover, we develop multiscale methods for identifying regions of monotonicity and a general procedure for detecting the modes of a multivariate density. It is shown that the latter method localizes the modes with an effectively optimal rate. The theoretical results are illustrated by means of a simulation study and a data example. The new method is applied to and motivated by the determination and verification of the position of high-energy sources from X-ray observations by the Swift satellite which is important for a multiwavelength analysis of objects such as Active Galactic Nuclei. © 2017 The Institute of Statistical Mathematics, Tokyo

In this paper, we present an innovative method for constructing proper priors for the skewness (shape) parameter in the skew-symmetric family of distributions. The proposed method is based on assigning a prior distribution on the perturbation effect of the shape parameter, which is quantified in terms of the total variation distance. We discuss strategies to translate prior beliefs about the asymmetry of the data into an informative prior distribution of this class. We show via a Monte Carlo simulation study that our non-informative priors induce posterior distributions with good frequentist properties, similar to those of the Jeffreys prior. Our informative priors yield better results than their competitors from the literature. We also propose a scale-invariant and location-invariant prior structure for models with unknown location and scale parameters and provide sufficient conditions for the propriety of the corresponding posterior distribution. Illustrative examples are presented using simulated and real data. © 2017 Board of the Foundation of the Scandinavian Journal of Statistics.

This paper is concerned with tests for changes in the jump behaviour of a time-continuous process. Based on results on weak convergence of a sequential empirical tail integral process, asymptotics of certain test statistics for breaks in the jump measure of an Itô semimartingale are constructed. Whenever limiting distributions depend in a complicated way on the unknown jump measure, empirical quantiles are obtained using a multiplier bootstrap scheme. An extensive simulation study shows a good performance of our tests in finite samples. © 2017 ISI/BS.

We derive optimal designs to estimate efficacy and toxicity in active controlled dose-finding trials when the bivariate continuous outcomes are described using nonlinear regression models. We determine upper bounds on the required number of different doses and provide conditions under which the boundary points of the design space are included in the optimal design.We provide an analytical description of minimally supported optimal designs and show that they do not depend on the correlation between the bivariate outcomes. © 2017 Biometrika Trust.

The problem under investigation is that of efficient statistical inference for comparing two regression curves estimated from two samples of dependent measurements. Based on a representation of the best pair of linear unbiased estimators in continuous time models as a stochastic integral, a pair of linear unbiased estimators with corresponding optimal designs for finite sample size is constructed. This pair minimises the width of the confidence band for the difference between the estimated curves in a class of linear unbiased estimators approximating the stochastic integrals and is very close to the pair of weighted least squares estimators with corresponding optimal design. Thus results readily available in the literature are extended to the case of correlated observations and an easily implementable solution is provided which is practically non distinguishable from the weighted least squares estimators. The advantages of using the proposed pairs of estimators with corresponding optimal designs for the comparison of regression models are illustrated via several numerical examples. © 2016 Elsevier B.V.

A common problem in Phase II clinical trials is the comparison of dose response curves corresponding to different treatment groups. If the effect of the dose level is described by parametric regression models and the treatments differ in the administration frequency (but not in the sort of drug), a reasonable assumption is that the regression models for the different treatments share common parameters. This paper develops optimal design theory for the comparison of different regression models with common parameters. We derive upper bounds on the number of support points of admissible designs, and explicit expressions for D-optimal designs are derived for frequently used dose response models with a common location parameter. If the location and scale parameter in the different models coincide, minimally supported designs are determined and sufficient conditions for their optimality in the class of all designs derived. The results are illustrated in a dose-finding study comparing monthly and weekly administration. © Institute of Mathematical Statistics, 2017.

We consider the problem of designing additional experiments to update statistical models for latent day specific effects. The problem appears in thermal spraying, where particles are sprayed on surfaces to obtain a coating. The relationships between in-flight properties of the particles and the controllable variables are modelled by generalized linear models. However, there are also non-controllable variables, which may vary from day to day and are modelled by day-specific additive effects. Existing generalized linear models for properties of the particles in flight must be updated on a limited number of additional experiments on a different day. We develop robust D-optimal designs to collect additional data for an update of the day effects, which are efficient for the estimation of the parameters in all models under consideration. The results are applied to the thermal spraying process and a comparison of the statistical analysis based on a reference design as well as on a selected Bayesian D-optimal design is performed. © 2016 Royal Statistical Society

Classical spectral methods are subject to two fundamental limitations: they can account only for covariance-related serial dependences, and they require second-order stationarity. Much attention has been devoted lately to quantile-based spectral methods that go beyond covariance-based serial dependence features. At the same time, covariance-based methods relaxing stationarity into much weaker local stationarity conditions have been developed for a variety of time series models. Here, we combine those two approaches by proposing quantile-based spectral methods for locally stationary processes. We therefore introduce a time varying version of the copula spectra that have been recently proposed in the literature, along with a suitable local lag window estimator. We propose a new definition of local strict stationarity that allows us to handle completely general non-linear processes without any moment assumptions, thus accommodating our quantile-based concepts and methods. We establish a central limit theorem for the new estimators and illustrate the power of the proposed methodology by means of a simulation study. Moreover, in two empirical studies (namely of the Standard & Poor's 500 series and a temperature data set recorded in Hohenpeissenberg), we demonstrate that the new approach detects important variations in serial dependence structures both across time and across quantiles. Such variations remain completely undetected and are actually undetectable, via classical covariance-based spectral methods. © 2017 The Royal Statistical Society and Blackwell Publishing Ltd.

The problem of constructing . T-optimal discriminating designs for Fourier regression models is considered. Explicit solutions of the optimal design problem for discriminating between two Fourier regression models, which differ by at most three trigonometric functions, are provided. In general, the . T-optimal discriminating design depends in a complicated way on the parameters of the larger model, and for special configurations of the parameters . T-optimal discriminating designs can be found analytically. Moreover, in the remaining cases this dependence is studied by calculating the optimal designs numerically. In particular, it is demonstrated that . D- and . Ds-optimal designs have rather low efficiencies with respect to the . T-optimality criterion. © 2016 Elsevier B.V.

Most of the literature on change point analysis by means of hypothesis testing considers hypotheses of the form H0:θ1=θ2versusH1:θ1≠θ2, where θ1 and θ2 denote parameters of the process before and after a change point. The paper takes a different perspective and investigates the null hypotheses of no relevant changes, i.e. H0:θ1-θ2≤Δ, where · is an appropriate norm. This formulation of the testing problem is motivated by the fact that in many applications a modification of the statistical analysis might not be necessary, if the difference between the parameters before and after the change point is small. A general approach to problems of this type is developed which is based on the cumulative sum principle. For the asymptotic analysis weak convergence of the sequential empirical process must be established under the alternative of non-stationarity, and it is shown that the resulting test statistic is asymptotically normally distributed. The results can also be used to establish similarity of the parameters, i.e. H1:θ1-θ2≤Δ, at a controlled type 1 error and to estimate the magnitudeθ1-θ2 of the change with a corresponding confidence interval. Several applications of the methodology are given including tests for relevant changes in the mean, variance, parameter in a linear regression model and distribution function among others. The finite sample properties of the new tests are investigated by means of a simulation study and illustrated by analysing a data example from portfolio management. © 2016 The Royal Statistical Society and Blackwell Publishing Ltd.

Background: Most statistical design and analysis methods for clinical trials have been developed and evaluated where at least several hundreds of patients could be recruited. These methods may not be suitable to evaluate therapies if the sample size is unavoidably small, which is usually termed by small populations. The specific sample size cut off, where the standard methods fail, needs to be investigated. In this paper, the authors present their view on new developments for design and analysis of clinical trials in small population groups, where conventional statistical methods may be inappropriate, e.g., because of lack of power or poor adherence to asymptotic approximations due to sample size restrictions. Method: Following the EMA/CHMP guideline on clinical trials in small populations, we consider directions for new developments in the area of statistical methodology for design and analysis of small population clinical trials. We relate the findings to the research activities of three projects, Asterix, IDeAl, and InSPiRe, which have received funding since 2013 within the FP7-HEALTH-2013-INNOVATION-1 framework of the EU. As not all aspects of the wide research area of small population clinical trials can be addressed, we focus on areas where we feel advances are needed and feasible. Results: The general framework of the EMA/CHMP guideline on small population clinical trials stimulates a number of research areas. These serve as the basis for the three projects, Asterix, IDeAl, and InSPiRe, which use various approaches to develop new statistical methodology for design and analysis of small population clinical trials. Small population clinical trials refer to trials with a limited number of patients. Small populations may result form rare diseases or specific subtypes of more common diseases. New statistical methodology needs to be tailored to these specific situations. Conclusion: The main results from the three projects will constitute a useful toolbox for improved design and analysis of small population clinical trials. They address various challenges presented by the EMA/CHMP guideline as well as recent discussions about extrapolation. There is a need for involvement of the patients' perspective in the planning and conduct of small population clinical trials for a successful therapy evaluation. © 2016 The Author(s).

In this paper we consider the problem of measuring stationarity in locally stationary long-memory processes. We introduce an L2-distance between the spectral density of the locally stationary process and its best approximation under the assumption of stationarity. The distance is estimated by a numerical approximation of the integrated spectral periodogram and asymptotic normality of the resulting estimate is established. The results can be used to construct a simple test for the hypothesis of stationarity in locally stationary long-range dependent processes. We also propose a bootstrap procedure to improve the approximation of the nominal level and prove its consistency. Throughout the paper, we work with Riemann sums of a squared periodogram instead of integrals (as it is usually done in the literature) and as a by-product of independent interest it is demonstrated that the two approaches behave differently in the limit.

A key objective of Phase II dose finding studies in clinical drug development is to adequately characterize the dose response relationship of a new drug. An important decision is then on the choice of a suitable dose response function to support dose selection for the subsequent Phase III studies. In this paper, we compare different approaches for model selection and model averaging using mathematical properties as well as simulations. We review and illustrate asymptotic properties of model selection criteria and investigate their behavior when changing the sample size but keeping the effect size constant. In a simulation study, we investigate how the various approaches perform in realistically chosen settings. Finally, the different methods are illustrated with a recently conducted Phase II dose finding study in patients with chronic obstructive pulmonary disease. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

A novel thermodynamic modeling strategy of stable solid alloy phases is proposed based on segmented regression approach. The model considers several physical effects (e.g. electronic, vibrational, etc.) and is valid from 0 K up to the melting temperature. The preceding approach has been applied for several pure elements. Results show good agreement with experimental data at low and high temperatures. Since it is not a first attempt to propose a “universal” physical-based model down to 0 K for the pure elements as an alternative to current SGTE description, we also compare the results to existing models. Analysis of the obtained results shows that the newly proposed model delivers more accurate description down to 0 K for all studied pure elements according to several statistical tests. © 2016 Elsevier Ltd

We consider the optimal design problem for a comparison of two regression curves, which is used to establish the similarity between the dose response relationships of two groups. An optimal pair of designs minimizes the width of the confidence band for the difference between the two regression functions. Optimal design theory (equivalence theorems, efficiency bounds) is developed for this non-standard design problem and for some commonly used dose response models optimal designs are found explicitly. The results are illustrated in several examples modeling dose response relationships. It is demonstrated that the optimal pair of designs for the comparison of the regression curves is not the pair of the optimal designs for the individual models. In particular, it is shown that the use of the optimal designs proposed in this paper instead of commonly used "non-optimal" designs yields a reduction of the width of the confidence band by more than 50%. © Institute of Mathematical Statistics, 2016.

In the one-parameter regression model with AR(1) and AR(2) errors we find explicit expressions and a continuous approximation of the optimal discrete design for the signed least square estimator. The results are used to derive the optimal variance of the best linear estimator in the continuous time model and to construct efficient estimators and corresponding optimal designs for finite samples. © 2016 Elsevier B.V..

This paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this challenging optimal design problem is given for a broad class of regression models and covariance kernels. We propose a class of estimators which are only slightly more complicated than the ordinary least-squares estimators. We then demonstrate that we can design the experiments, such that asymptotically the new estimators achieve the same precision as the best linear unbiased estimator computed for the whole trajectory of the process. As a by-product, we derive explicit expressions for the BLUE in the continuous time model and analytic expressions for the optimal designs in a wide class of regression models. We also demonstrate that for a finite number of observations the precision of the proposed procedure, which includes the estimator and design, is very close to the best achievable. The results are illustrated on a few numerical examples.

Quantile-and copula-related spectral concepts recently have been considered by various authors. Those spectra, in their most general form, provide a full characterization of the copulas associated with the pairs (Xt,Xt-k) in a process (Xt )t Z, and account for important dynamic features, such as changes in the conditional shape (skewness, kurtosis), time-irreversibility, or dependence in the extremes that their traditional counterparts cannot capture. Despite various proposals for estimation strategies, only quite incomplete asymptotic distributional results are available so far for the proposed estimators, which constitutes an important obstacle for their practical application. In this paper, we provide a detailed asymptotic analysis of a class of smoothed rank-based cross-periodograms associated with the copula spectral density kernels introduced in Dette et al. [Bernoulli 21 (2015) 781-831].We show that, for a very general class of (possibly nonlinear) processes, properly scaled and centered smoothed versions of those cross-periodograms, indexed by couples of quantile levels, converge weakly, as stochastic processes, to Gaussian processes. A first application of those results is the construction of asymptotic confidence intervals for copula spectral density kernels. The same convergence results also provide asymptotic distributions (under serially dependent observations) for a new class of rank-based spectral methods involving the Fourier transforms of rank-based serial statistics such as the Spearman, Blomqvist or Gini autocovariance coefficients. © 2016 ISI/BS.

We consider the problem of estimating an additive regression function in an inverse regression model with a convolution type operator. A smooth backfitting procedure is developed and asymptotic normality of the resulting estimator is established. Compared to other methods for the estimation in additive models the new approach neither requires observations on a regular grid nor the estimation of the joint density of the predictor. It is also demonstrated by means of a simulation study that the backfitting estimator outperforms the marginal integration method at least by a factor of two with respect to the integrated mean squared error criterion. The methodology is illustrated by a problem of live cell imaging in fluorescence microscopy. © 2015, The Institute of Statistical Mathematics, Tokyo.

For a sample of n independent identically distributed p-dimensional centered random vectors with covariance matrix σn let S~n denote the usual sample covariance (centered by the mean) and Sn the non-centered sample covariance matrix (i.e. the matrix of second moment estimates), where p>n. In this paper, we provide the limiting spectral distribution and central limit theorem for linear spectral statistics of the Moore-Penrose inverse of Sn and S~n. We consider the large dimensional asymptotics when the number of variables p→∞ and the sample size n→∞ such that p/n→c∈(1, +∞). We present a Marchenko-Pastur law for both types of matrices, which shows that the limiting spectral distributions for both sample covariance matrices are the same. On the other hand, we demonstrate that the asymptotic distribution of linear spectral statistics of the Moore-Penrose inverse of S~n differs in the mean from that of Sn. © 2016 Elsevier Inc.

This paper is concerned with testing a core economic restriction, negative semidefiniteness of the Slutsky matrix. We consider a system of nonseparable structural equations with infinite dimensional unobservables, and employ quantile regression methods because they allow us to utilize the entire distribution of the data. Difficulties arise because the restriction involves several equations, while the quantile is a univariate concept. We establish that we may use quantiles of linear combinations of the dependent variable, develop a new empirical process based test that applies kernel quantile estimators, and investigate its finite and large sample behavior. Finally, we apply all concepts to Canadian microdata. © 2015 Elsevier B.V. All rights reserved.

The problem of constructing Bayesian optimal discriminating designs for a class of regression models with respect to the T -optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 57-70] is considered. It is demonstrated that the discretization of the integral with respect to the prior distribution leads to locally T -optimal discriminating design problems with a large number of model comparisons. Current methodology for the numerical construction of discrimination designs can only deal with a few comparisons, but the discretization of the Bayesian prior easily yields to discrimination design problems for more than 100 competing models. A new efficient method is developed to deal with problems of this type. It combines some features of the classical exchange type algorithm with the gradient methods. Convergence is proved, and it is demonstrated that the new method can find Bayesian optimal discriminating designs in situations where all currently available procedures fail. © Institute of Mathematical Statistics, 2015.

Uniform asymptotic confidence bands for a multivariate regression function in an inverse regression model with a convolution-type operator are constructed. The results are derived using strong approximation methods and a limit theorem for the supremum of a stationary Gaussian field over an increasing system of sets. As a particular application, asymptotic confidence bands for a time dependent regression function ft (x) (x ∈ Rd, t ∈ R) in a convolution-type inverse regression model are obtained. Finally, we demonstrate the practical feasibility of our proposed methods in a simulation study and an application to the estimation of the luminosity profile of the elliptical galaxy NGC5017. To the best knowledge of the authors, the results presented in this paper are the first which provide uniform confidence bands for multivariate nonparametric function estimation in inverse problems. © 2015 ISI/BS.

Optimal design of dose-finding studies with an active control has only been considered in the literature for regression models with normally distributed errors and known variances, where the focus is on estimating the smallest dose that achieves the same treatment effect as the active control. This paper discusses such dose-finding studies from a broader perspective. We consider a general class of optimality criteria and models arising from an exponential family. Optimal designs are constructed for several situations and their efficiency is illustrated with examples. © 2015 Biometrika Trust.

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start to change. In many cases, it is of interest to locate the time point where the properties start to vary. In contrast to the analysis of abrupt changes, methods for detecting smooth or gradual change points are less developed and often require strong parametric assumptions. In this paper, we develop a fully nonparametric method to estimate a smooth change point in a locally stationary framework. We set up a general procedure which allows us to deal with a wide variety of stochastic properties including the mean, (auto)covariances and higher moments. The theoretical part of the paper establishes the convergence rate of the new estimator. In addition, we examine its finite sample performance by means of a simulation study and illustrate the methodology by two applications to financial return data. © Institute of Mathematical Statistics, 2015.

We propose a new nonparametric procedure (referred to as MuBreD) for the detection and estimation of multiple structural breaks in the autocovariance function of a multivariate (second-order) piecewise stationary process, which also identifies the components of the series where the breaks occur. MuBreD is based on a comparison of the estimated spectral distribution on different segments of the observed time series and consists of three steps: it starts with a consistent test, which allows us to prove the existence of structural breaks at a controlled Type I error. Second, it estimates sets containing possible break points and finally these sets are reduced to identify the relevant structural breaks and corresponding components which are responsible for the changes in the autocovariance structure. In contrast to all other methods proposed in the literature, our approach does not make any parametric assumptions, is not especially designed for detecting one single change point, and addresses the problem of multiple structural breaks in the autocovariance function directly with no use of the binary segmentation algorithm. We prove that the new procedure detects all components and the corresponding locations where structural breaks occur with probability converging to one as the sample size increases and provide data-driven rules for the selection of all regularization parameters. The results are illustrated by analyzing financial asset returns, and in a simulation study it is demonstrated that MuBreD outperforms the currently available nonparametric methods for detecting breaks in the dependency structure of multivariate time series. Supplementary materials for this article are available online. © 2015 American Statistical Association.

We investigate likelihood ratio contrast tests for dose response signal detection under model uncertainty, when several competing regression models are available to describe the dose response relationship. The proposed approach uses the complete structure of the regression models, but does not require knowledge of the parameters of the competing models. Standard likelihood ratio test theory is applicable in linear models as well as in nonlinear regression models with identifiable parameters. However, for many commonly used nonlinear dose response models the regression parameters are not identifiable under the null hypothesis of no dose response and standard arguments cannot be used to obtain critical values. We thus derive the asymptotic distribution of likelihood ratio contrast tests in regression models with a lack of identifiability and use this result to simulate the quantiles based on Gaussian processes. The new method is illustrated with a real data example and compared to existing procedures using theoretical investigations as well as simulations. © 2015, The International Biometric Society.

We consider the construction of optimal designs for nonlinear regression models when there are measurement errors in the covariates. Corresponding approximate design theory is developed for maximum likelihood and least-squares estimation, with the latter leading to nonconcave optimization problems. Analytical characterizations of the locally D-optimal saturated designs are provided for the Michaelis-Menten, Emax and exponential regression models. Through concrete applications, we illustrate how measurement errors in the covariates affect the optimal choice of design and show that the locally D-optimal saturated designs are highly efficient for relatively small misspecifications of the parameter values. © 2015 Biometrika Trust.

In this paper, we present an alternative method for the spectral analysis of a univariate, strictly stationary time series {Y<inf>t</inf>}<inf>t∈ℤ</inf>. We define a "new" spectrum as the Fourier transform of the differences between copulas of the pairs (Y<inf>t</inf>, Y<inf>t-k</inf>) and the independence copula. This object is called a copula spectral density kernel and allows to separate the marginal and serial aspects of a time series. We show that this spectrum is closely related to the concept of quantile regression. Like quantile regression, which provides much more information about conditional distributions than classical location-scale regression models, copula spectral density kernels are more informative than traditional spectral densities obtained from classical autocovariances. In particular, copula spectral density kernels, in their population versions, provide (asymptotically provide, in their sample versions) a complete description of the copulas of all pairs (Y<inf>t</inf>, Y<inf>t-k</inf>). Moreover, they inherit the robustness properties of classical quantile regression, and do not require any distributional assumptions such as the existence of finite moments. In order to estimate the copula spectral density kernel, we introduce rank-based Laplace periodograms which are calculated as bilinear forms of weighted L<inf>1</inf>-projections of the ranks of the observed time series onto a harmonic regression model. We establish the asymptotic distribution of those periodograms, and the consistency of adequately smoothed versions. The finite-sample properties of the new methodology, and its potential for applications are briefly investigated by simulations and a short empirical example. © 2015 ISI/BS.

In this article, we consider locally optimal designs problems for rational regression models. In the case where the degrees of polynomials in the numerator and denominator differ by at most 1, we identify an invariance property of the optimal designs if the denominator polynomial is palindromic, which reduces the optimization problem by 50%. The results clarify and extend the particular structure of locally c-, D-, and E-optimal designs for inverse quadratic regression models that have been found by Haines (1992) and have recently been extended by Dette and Kiss (2009). We also investigate the relation between the D-optimal designs for the Michaelis-Menten and EMAX models from a more general point of view. The results are illustrated by several examples. © Grace Scientific Publishing, LLC.

We conduct an empirical study using the quantile-based correlation function to uncover the temporal dependencies in financial time series. The study uses intraday data for the S&P500 stocks from the New York Stock Exchange (NYSE). After establishing an empirical overview, we compare the quantile-based correlation function to stochastic processes from the GARCH family and find striking differences. This motivates us to propose the quantile-based correlation function as a powerful tool to assess the agreements between stochastic processes and empirical data.

In this article, we propose a new test for additivity in nonparametric quantile regression with a high-dimensional predictor. Asymptotic normality of the corresponding test statistic (after appropriate standardization) is established under the null hypothesis, local and fixed alternatives. We also propose a bootstrap procedure which can be used to improve the approximation of the nominal level for moderate sample sizes. The methodology is also illustrated by means of a small simulation study, and a data example is analyzed. © 2014, The Institute of Statistical Mathematics, Tokyo.

The problem of determining optimal designs for least squares estimation is considered in the common linear regression model with correlated observations. The approach is based on the determination of 'nearly' universally optimal designs, even in the case where the universally optimal design does not exist. For this purpose, a new optimality criterion which reflects the distance between a given design and an ideal universally optimal design is introduced. A necessary condition for the optimality of a given design is established. Numerical methods for constructing these designs are proposed and applied for the determination of optimal designs in a number of specific instances. The results indicate that the new 'nearly' universally optimal designs have good efficiencies with respect to common optimality criteria. © 2013 Elsevier Inc. All rights reserved.

In a recent paper Birke and Bissantz (2009) considered the problem of nonparametric estimation in inverse regression models with convolution-type operators. For multivariate predictors nonparametric methods suffer from the curse of dimensionality and we consider inverse regression models with the additional qualitative assumption of additivity. In these models several additive estimators are studied. In particular, we propose a new estimation method for observations on regular spaced grid and investigate estimators under the random design assumption which are applicable when observations are not available on a grid. Finally, we compare these estimators with the marginal integration and the non-additive estimator by means of a simulation study. It is demonstrated that the new method yields a substantial improvement of the currently available procedures.

We consider quantile regression processes from censored data under dependent data structures and derive a uniform Bahadur representation for those processes. We also consider cases where the dimension of the parameter in the quantile regression model is large. It is demonstrated that traditional penalization methods such as the adaptive lasso yield suboptimal rates if the coefficients of the quantile regression cross zero. New penalization techniques are introduced which are able to deal with specific problems of censored data and yield estimates with an optimal rate. In contrast to most of the literature, the asymptotic analysis does not require the assumption of independent observations, but is based on rather weak assumptions, which are satisfied for many kinds of dependent data.

In this paper we define distributions on the moment spaces corresponding to p × p real or complex matrix measures on the real line with an unbounded support. For random vectors on the unbounded matricial moment spaces we prove the convergence in distribution to the Gaussian orthogonal ensemble or the Gaussian unitary ensemble, respectively. © 2014 Elsevier Inc.

E-optimal experimental designs for a second-order response surface model with k ≥ 1 predictors are investigated. If the design space is the k-dimensional unit cube, Galil and Kiefer [J. Statist. Plann. Inference 1 (1977a) 121-132] determined optimal designs in a restricted class of designs (defined by the multiplicity of the minimal eigenvalue) and stated their universal optimality as a conjecture. In this paper, we prove this claim and show that these designs are in fact E-optimal in the class of all approximate designs. Moreover, if the design space is the unit ball, E-optimal designs have not been found so far and we also provide a complete solution to this optimal design problem. The main difficulty in the construction of E-optimal designs for the second-order response surface model consists in the fact that for the multiplicity of the minimum eigenvalue of the "optimal information matrix" is larger than one (in contrast to the case k = 1) and as a consequence the corresponding optimality criterion is not differentiable at the optimal solution. These difficulties are solved by considering nonlinear Chebyshev approximation problems, which arise from a corresponding equivalence theorem. The extremal polynomials which solve these Chebyshev problems are constructed explicitly leading to a complete solution of the corresponding E-optimal design problems. © Institute of Mathematical Statistics, 2014.

We consider the problem of model selection for quantile regression analysis when a particular purpose of the modeling procedure has to be taken into account. Typical examples include estimation of the area under the curve in pharmacokinetics or estimation of the minimum effective dose in phase II clinical trials. A focused information criterion for quantile regression is developed, analyzed, and investigated by means of a simulation study and data analysis.

Dose finding studies often compare several doses of a new compound with a marketed standard treatment as an active control. In the past, however, research has focused mostly on experimental designs for placebo controlled dose finding studies. To the best of our knowledge, optimal designs for dose finding studies with an active control have not been considered so far. As the statistical analysis for an active controlled dose finding study can be formulated in terms of a mixture of two regression models, the related design problem is different from what has been investigated before in the literature. We present a rigorous approach to the problem of determining optimal designs for estimating the smallest dose achieving the same treatment effect as the active control. We determine explicitly the locally optimal designs for a broad class of models employed in such studies. We also discuss robust design strategies and determine related Bayesian and standardized minimax optimal designs. We illustrate the results by investigating alternative designs for a clinical trial which has recently appeared in a consulting project of one of the authors. © 2013 Royal Statistical Society.

In nonlinear regression models the Fisher information depends on the parameters of the model. Consequently, optimal designs maximizing some functional of the information matrix cannot be implemented directly but require some preliminary knowledge about the unknown parameters. Bayesian optimality criteria provide an attractive solution to this problem. These criteria depend sensitively on a reasonable specification of a prior distribution for the model parameters which might not be available in all applications. In this paper we investigate Bayesian optimality criteria with non-informative prior distributions. In particular, we study the Jeffreys and the Berger-Bernardo prior for which the corresponding optimality criteria are not necessarily concave. Several examples are investigated where optimal designs with respect to these criteria are calculated and compared to Bayesian optimal designs based on a uniform and a functional uniform prior. © 2014.

In this paper we investigate the problem of designing experiments for generalized least-squares analysis in the Michaelis–Menten model. We study the structure of exact D-optimal designs in a model with an autoregressive error structure. Explicit results for locally D-optimal designs are derived for the case where two observations can be taken per subject. Additionally standardized maximin D-optimal designs are obtained in this case. The results illustrate the enormous difficulties to find exact optimal designs explicitly for nonlinear regression models with correlated observations. © 2013, © 2013 Taylor & Francis.

In a recent article, Noh, El Ghouch, and Bouezmarni proposed a new semiparametric estimate of a regression function with a multivariate predictor, which is based on a specification of the dependence structure between the predictor and the response by means of a parametric copula. This comment investigates the effect which occurs under misspecification of the parametric model. We demonstrate by means of several examples that even for a one or two-dimensional predictor the error caused by a “wrong” specification of the parametric family is rather severe, if the regression is not monotone in one of the components of the predictor. Moreover, we also show that these problems occur for all of the commonly used copula families and we illustrate in several examples that the copula-based regression may lead to invalid results even when flexible copula models such as vine copulas (with the common parametric families) are used in the estimation procedure. © 2014 American Statistical Association.

This article presents a framework for comparing bivariate distributions according to their degree of regression dependence. We introduce the general concept of a regression dependence order (RDO). In addition, we define a new non-parametric measure of regression dependence and study its properties. Besides being monotone in the new RDOs, the measure takes on its extreme values precisely at independence and almost sure functional dependence, respectively. A consistent non-parametric estimator of the new measure is constructed and its asymptotic properties are investigated. Finally, the finite sample properties of the estimate are studied by means of a small simulation study. © 2012 Board of the Foundation of the Scandinavian Journal of Statistics.

In this paper we investigate the problem of testing the assumption of stationarity in locally stationary processes. The test is based on an estimate of a Kolmogorov-Smirnov type distance between the true time varying spectral density and its best approximation through a stationary spectral density. Convergence of a time varying empirical spectral process indexed by a class of certain functions is proved, and furthermore the consistency of a bootstrap procedure is shown which is used to approximate the limiting distribution of the test statistic. Compared to other methods proposed in the literature for the problem of testing for stationarity the new approach has at least two advantages: On one hand, the test can detect local alternatives converging to the null hypothesis at any rate gT → 0 such that gT T1/2 → ∞, where T denotes the sample size. On the other hand, the estimator is based on only one regularization parameter while most alternative procedures require two. Finite sample properties of the method are investigated by means of a simulation study, and a comparison with several other tests is provided which have been proposed in the literature. © 2013 ISI/BS.

Background: In type 2 diabetes mellitus, treatment with insulin is initiated when HbA1c is reduced inadequately with oral antidiabetic drugs or incretin mimetics. Whether insulin analogues vs. regular human insulin have favorable effects in terms of efficacy and metabolism is under discussion. Patients: 29 patients with type 2 diabetes mellitus (19 males, 10 females) with a mean age 59±11(mean±SD) years (range 24-75) and treated with oral drugs for at least 6 months and a HbA1c >7.0% were included in an open, randomised, prospective, controlled, multicenter parallel-group study over a period of 24 months. Methods: 11 patients were randomized in the regular human insulin-group (RHI-group) and 18 patients in the insulin aspart group (IA-group). Insulin aspart or regular human insulin should be treated to <140 mg/dl postprandial and insulin detemir should be treated to <110 mg/dl in the morning (fasting) after a previous dose titration of insulin aspart or regular human insulin over 6 months of treatment. Adiponectin, HbA1c, fasting plasma glucose, BMI, triglycerides and cholesterol levels were determined every 3 months. Results: 7/11 of the RHI-group received additional insulin detemir and 13/18 of the IA-group. HbA1c levels decreased significantly in both groups (8.7±1.6 to 7.2±0.9 in the RHI-group (p<0.05) vs. 8.7±1.6 to7.3±0.9 in the IA-group (p<0.05)) without significant difference between the groups. No significant changes were seen between the 2 groups during the 24 months period in terms of BMI, fasting plasma glucose, lipids. Adiponectin serum levels decreased over the time without difference between the groups (7.9±4.0 to 5.0±2.0 in the RHI-group (p<0.03) vs. 7.3±3.4 to 4.8±2.8 in the IA-group (p<0.0001)). During the first 9 months, the insulin dosage to reach the postprandial blood glucose <140 mg/dl, were significantly lower in the IA-group, but approached the following the RHI-group without significant changes after 24 months. Conclusion: After stopping oral antidiabetic drugs in type 2 diabetes mellitus, insulin aspart in comparison to human regular insulin decreased effectively HbA1c levels without significant difference. Moreover, insulin aspart in comparison to human regular insulin does not have any substantial benefits concerning metabolic effects and adipocytokines in type 2 diabetes mellitus over a 24 months treatment period. © J. A. Barth Verlag in Georg Thieme Verlag KG Stuttgart · New York.

In a recent paper Yang and Stufken [Ann. Statist. 40 (2012a) 1665-1685] gave sufficient conditions for complete classes of designs for nonlinear regression models. In this note we demonstrate that there is an alternative way to validate this result. Our main argument utilizes the fact that boundary points of moment spaces generated by Chebyshev systems possess unique representations. © 2013 Institute of Mathematical Statistics.

In contrast to conventional model selection criteria, the Focused Information Criterion (FIC) allows for the purpose-specific choice of model specifications. This accommodates the idea that one kind of model might be highly appropriate for inferences on a particular focus parameter, but not for another. Ever since its development, the FIC has been increasingly applied in the realm of statistics, but this concept appears to be virtually unknown in the literature on energy and production economics. Using the classical example of the Translog cost function and production data for 35 U.S. industry sectors (1960-2005), this paper provides for an empirical illustration of the FIC and demonstrates its usefulness in selecting production models, thereby focusing on the ease of substitution between energy and capital versus energy and labor. © 2013 Elsevier B.V.

In a recent paper Fay and Philippe [ESAIM: PS 6 (2002) 239–258] proposed a goodness-offit test for long-range dependent processes which uses the logarithmic contrast as information measure. These authors established asymptotic normality under the null hypothesis and local alternatives. In the present note we extend these results and show that the corresponding test statistic is also normally distributed under fixed alternatives. © EDP Sciences, SMAI 2013.

This contribution gives a brief review on penalized least squares methods in sparse linear regression models with a specific focus on heteroscedastic data structures. We discuss the well known bridge estimators, Lasso and adaptive Lasso and a new class of weighted penalized least squares methods, which address the problem of heteroscedasticity. We give a careful explanation on how the choice of the regularizing parameter affects the quality of the statistical inference (such as conservative or consistent model selection). The new estimators are asymptotically (pointwise) as efficient as estimators which are assisted by a model selection oracle. The results are illustrated by means of a small simulation study and the analysis of a data example. © Springer-Verlag Berlin Heidelberg 2013.

For the problem of estimating lower tail and upper tail copulas, we propose two bootstrap procedures for approximating the distribution of the corresponding empirical tail copulas. The first method uses a multiplier bootstrap of the empirical tail copula process and requires estimation of the partial derivatives of the tail copula. The second method avoids this estimation problem and uses multipliers in the two-dimensional empirical distribution function and in the estimates of the marginal distributions. For both multiplier bootstrap procedures, we prove consistency. For these investigations, we demonstrate that the common assumption of the existence of continuous partial derivatives in the the literature on tail copula estimation is so restrictive, such that the tail copula corresponding to tail independence is the only tail copula with this property. Moreover, we are able to solve this problem and prove weak convergence of the empirical tail copula process under nonrestrictive smoothness assumptions that are satisfied for many commonly used models. These results are applied in several statistical problems, including minimum distance estimation and goodness-of-fit testing. © 2013 ISI/BS.

A new test for comparing conditional quantile curves is proposed which is able to detect Pitman alternatives converging to the null hypothesis at the optimal rate. The basic idea of the test is to measure differences between the curves by a process of integrated nonparametric estimates of the quantile curve. We prove weak convergence of this process to a Gaussian process and study the finite sample properties of a Kolmogorov-Smirnov test by means of a simulation study. © 2013 Copyright Taylor and Francis Group, LLC.

We consider the problem of nonparametric quantile regression for twice censored data. Two new estimates are presented, which are constructed by applying concepts of monotone rearrangements to estimates of the conditional distribution function. The proposed methods avoid the problem of crossing quantile curves. Weak uniform consistency and weak convergence is established for both estimates and their finite sample properties are investigated by means of a simulation study. As a by-product, we obtain a new result regarding the weak convergence of the Beran estimator for right censored data on the maximal possible domain, which is of its own interest. © 2013 ISI/BS.

In this paper, we investigate the efficiency of response-adaptive locally optimum designs. We focus on two-stage adaptive designs, where after the first stage the accrued data are used to determine a locally optimum design for the second stage. On the basis of an explicit expansion of the information matrix, we compare the variance of the maximum likelihood estimates obtained from a two-stage adaptive design and a fixed design without adaptation. For several one-parameter models, we provide explicit expressions for the relative efficiency of these two designs, which is seen to depend sensitively on the statistical problem under investigation. In particular, we show that in non-linear regression models with moderate or large variances the first-stage sample size of an adaptivedesign should be chosen sufficiently large in order to address variability in the interim parameter estimates. These findings support the results of recent simulation studies conducted to compare adaptive designs in more complex situations. We finally present an application to a real clinical dose-finding trial aiming at the estimation of the smallest dose achieving a certain percentage of the maximum treatment effect by using a three-parameter Emax model. © 2012 John Wiley & Sons, Ltd.

In the common linear regression model the problem of determining optimal designs for least squares estimation is considered in the case where the observations are correlated. A necessary condition for the optimality of a given design is provided, which extends the classical equivalence theory for optimal designs in models with uncorrelated errors to the case of dependent data. If the regression functions are eigenfunctions of an integral operator defined by the covariance kernel, it is shown that the corresponding measure defines a universally optimal design. For several models universally optimal designs can be identified explicitly. In particular, it is proved that the uniform distribution is universally optimal for a class of trigonometric regression models with a broad class of covariance kernels and that the arcsine distribution is universally optimal for the polynomial regression model with correlation structure defined by the logarithmic potential. To the best knowledge of the authors these findings provide the first explicit results on optimal designs for regression models with correlated observations, which are not restricted to the location scale model. © 2013 Institute of Mathematical Statistics.

In this article we consider the problem of constructing optimal designs for models with a constant coefficient of variation. We explore the special structure of the information matrix in these models and derive a characterization of optimal designs in the sense of Kiefer and Wolfowitz (1960) Besides locally optimal designs, Bayesian and standardized minimax optimal designs are also considered. Particular attention is spent on the problem of constructing D-optimal designs. The results are illustrated in several examples where optimal designs are calculated analytically and numerically. © 2013 Copyright Grace Scientific Publishing, LLC.

The problem of constructing optimal discriminating designs for a class of regression models is considered. We investigate a version of the Tpoptimality criterion as introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 289-303]. The numerical construction of optimal designs is very hard and challenging, if the number of pairwise comparisons is larger than 2. It is demonstrated that optimal designs with respect to this type of criteria can be obtained by solving (nonlinear) vector-valued approximation problems. We use a characterization of the best approximations to develop an efficient algorithm for the determination of the optimal discriminating designs. The new procedure is compared with the currently available methods in several numerical examples, and we demonstrate that the new method can find optimal discriminating designs in situations where the currently available procedures fail. © Institute of Mathematical Statistics, 2013.

This paper considers the problem of constructing optimal discriminating experimental designs for competing regression models on the basis of the T -optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 57-70]. T -optimal designs depend on unknown model parameters and it is demonstrated that these designs are sensitive with respect to misspecification. As a solution to this problem we propose a Bayesian and standardized maximin approach to construct robust and efficient discriminating designs on the basis of the T -optimality criterion. It is shown that the corresponding Bayesian and standardized maximin optimality criteria are closely related to linear optimality criteria. For the problem of discriminating between two polynomial regression models which differ in the degree by two the robust T -optimal discriminating designs can be found explicitly. The results are illustrated in several examples. © Institute of Mathematical Statistics, 2013.

We consider the problem of testing significance of predictors in multivariate nonparametric quantile regression. A stochastic process is proposed, which is based on a comparison of the responses with a nonparametric quantile regression estimate under the null hypothesis. It is demonstrated that under the null hypothesis this process converges weakly to a centered Gaussian process and the asymptotic properties of the test under fixed and local alternatives are also discussed. In particular we show, that - in contrast to the nonparametric approach based on estimation of L2 - distances - the new test is able to detect local alternatives which converge to the null hypothesis with any rate an→ 0 such that an √ n → ∞ (here n denotes the sample size). We also present a small simulation study illustrating the finite sample properties of a bootstrap version of the corresponding Kolmogorov-Smirnov test.

In this paper, we investigate the problem of testing semiparametric hypotheses in locally stationary processes. The proposed method is based on an empirical version of the L2-distance between the true time varying spectral density and its best approximation under the null hypothesis. As this approach only requires estimation of integrals of the time varying spectral density and its square, we do not have to choose a smoothing bandwidth for the local estimation of the spectral density - in contrast to most other procedures discussed in the literature. Asymptotic normality of the test statistic is derived both under the null hypothesis and the alternative. We also propose a bootstrap procedure to obtain critical values in the case of small sample sizes. Additionally, we investigate the finite sample properties of the new method and compare it with the currently available procedures by means of a simulation study. Finally, we illustrate the performance of the new test in two data examples, one regarding log returns of the S&P 500 and the other a well-known series of weekly egg prices. © 2012 Board of the Foundation of the Scandinavian Journal of Statistics.

In this paper we study the asymptotic properties of the adaptive Lasso estimate in high-dimensional sparse linear regression models with heteroscedastic errors. It is demonstrated that model selection properties and asymptotic normality of the selected parameters remain valid but with a suboptimal asymptotic variance. A weighted adaptive Lasso estimate is introduced and investigated. In particular, it is shown that the new estimate performs consistent model selection and that linear combinations of the estimates corresponding to the non-vanishing components are asymptotically normally distributed with a smaller variance than those obtained by the "classical" adaptive Lasso. The results are illustrated in a data example and by means of a small simulation study. © 2013 Allerton Press, Inc.

In this paper the inverse regression model Y=(f*ψ)(x)+ε is considered with a random error ε and a multivariate predictor x∈R d. In the model of interest the operation * denotes convolution, ψ is a given function and the object of interest is the function f itself, while the data only give direct, empirical access to f * ψ. In this setting asymptotic uniform confidence bands for the function f based on a kernel type estimator and a limit theorem given in [1] for the supremum of a stationary Gaussian field with compactly supported covariance function over an increasing system of sets are constructed. © 2012 American Institute of Physics.

In a recent paper, Eichler (2008) [11] considered a class of non- and semiparametric hypotheses in multivariate stationary processes, which are characterized by a functional of the spectral density matrix. The corresponding statistics are obtained using kernel estimates for the spectral distribution and are asymptotically normally distributed under the null hypothesis and local alternatives. In this paper, we derive the asymptotic properties of these test statistics under fixed alternatives. In particular, we also show weak convergence but with a different rate compared to the null hypothesis. We also discuss potential statistical applications of the asymptotic theory by means of a small simulation study. © 2011 Elsevier Inc.

We propose a new test for the hypothesis that a bivariate copula is an Archimedean copula which can be used as a preliminary step before further dependence modeling. The corresponding test statistic is based on a combination of two measures resulting from the characterization of Archimedean copulas by the property of associativity and by a strict upper bound on the diagonal by the Fréchet-Hoeffding upper bound. We prove weak convergence of this statistic and show that the critical values of the corresponding test can be determined by the multiplier bootstrap method. The test is shown to be consistent against all departures from Archimedeanity. A simulation study is presented which illustrates the finite-sample properties of the new test. © 2012 Elsevier Inc.

In this paper we investigate penalized least squares methods in linear regression models with heteroscedastic error structure. It is demonstrated that the basic properties with respect to model selection and parameter estimation of bridge estimators, Lasso and adaptive Lasso do not change if the assumption of homoscedasticity is violated. However, these estimators do not have oracle properties in the sense of Fan and Li (2001) if the oracle is based on weighted least squares. In order to address this problem we introduce weighted penalized least squares methods and demonstrate their advantages by asymptotic theory and by means of a simulation study. © 2012 Allerton Press, Inc.

In contrast to conventional measures, the Focused Information Criterion (FIC) allows the purpose-specific selection of models, thereby reflecting the idea that one kind of model might be appropriate for inferences on a parameter of interest, but not for another. Ever since its invention, the FIC has been increasingly applied in the realm of statistics, but this concept appears to be virtually unknown in the economic literature. Using a straightforward analytical example, this paper provides for a didactic illustration of the FIC and demonstrates its usefulness in economic applications. © 2011 Elsevier B.V.

In this paper we define distributions on moment spaces corresponding to measures on the real line with an unbounded support. We identify these distributions as limiting distributions of random moment vectors defined on compact moment spaces and as distributions corresponding to random spectral measures associated with the Jacobi, Laguerre and Hermite ensemble from random matrix theory. For random vectors on the unbounded moment spaces we prove a central limit theorem where the centering vectors correspond to the moments of the Marchenko-Pastur distribution and Wigner's semi-circle law. © Institute of Mathematical Statistics, 2012.

Random effects models are widely used in population pharmacokinetics and dose-finding studies. However, when more than one observation is taken per patient, the presence of correlated observations (due to shared random effects and possibly residual serial correlation) usually makes the explicit determination of optimal designs difficult. In this article, we introduce a class of multiplicative algorithms to be able to handle correlated data and thus allow numerical calculation of optimal experimental designs in such situations. In particular, we demonstrate its application in a concrete example of a crossover dose-finding trial, as well as in a typical population pharmacokinetics example. Additionally, we derive a lower bound for the efficiency of any given design in this context, which allows us on the one hand to monitor the progress of the algorithm, and on the other hand to investigate the efficiency of a given design without knowing the optimal one. Finally, we extend the methodology such that it can be used to determine optimal designs if there exist some requirements regarding the minimal number of treatments for several (in some cases all) experimental conditions. © 2011, The International Biometric Society.

We consider the moment space M n corresponding to p×p real or complex matrix measures defined on the interval [0,1]. The asymptotic properties of the first k components of a uniformly distributed vector (S 1,n,...,S n,n)*~U(M n)are studied as n→∞. In particular, it is shown that an appropriately centered and standardized version of the vector (S 1,n,...,S k,n) * converges weakly to a vector of k independent p×p Gaussian ensembles. For the proof of our results, we use some new relations between ordinary moments and canonical moments of matrix measures which are of their own interest. In particular, it is shown that the first k canonical moments corresponding to the uniform distribution on the real or complex moment space M n are independent multivariate Beta-distributed random variables and that each of these random variables converges in distribution (as the parameters converge to infinity) to the Gaussian orthogonal ensemble or to the Gaussian unitary ensemble, respectively. © 2011 Springer Science+Business Media, LLC.

We consider the problem of testing the parametric form of the volatility for high frequency data. It is demonstrated that in the presence of microstructure noise commonly used tests do not keep the preassigned level and are inconsistent. The concept of preaveraging is used to construct new tests, which do not suffer from these drawbacks. These tests are based on a Kolmogorov-Smirnov or Cramér-von-Mises functional of an integrated stochastic process, for which weak convergence to a (conditional) Gaussian process is established. The finite sample properties of a bootstrap version of the test are illustrated by means of a simulation study. © 2012 ISI/BS.

We consider the problem of testing parametric assumptions in an inverse regression model with a convolution-type operator. An L 2-type goodness-of-fit test is proposed which compares the distance between a parametric and a non-parametric estimate of the regression function. Asymptotic normality of the corresponding test statistic is shown under the null hypothesis and under a general non-parametric alternative with different rates of convergence in both cases. The feasibility of the proposed test is demonstrated by means of a small simulation study. In particular, the power of the test against certain types of alternative is investigated. Finally, an empirical example is provided, in which the proposed methods are applied to the determination of the shape of the luminosity profile of the elliptical galaxy NGC 5017. © 2012 Board of the Foundation of the Scandinavian Journal of Statistics.

We consider two frequently used PK/PD models and provide closed form descriptions of locally optimal designs for estimating individual parameters. In a novel way, we use these optimal designs and construct locally standardized maximin optimal designs for estimating any subset of the model parameters of interest. We do this by maximizing the minimal efficiency of the estimates across all relevant parameters so that these optimal designs are less dependent on the individual parameter or parameters of interest. Additionally, robust designs are proposed to further reduce the dependence on the nominal values of the parameters. We compare efficiencies of our proposed optimal designs with locally optimal designs and designs used in four real studies from the literature and show that our proposed designs provide advantages over those used in practice. © Springer Science+Business Media, LLC 2012.

Despite their importance, optimal designs for quantile regression models have not been developed so far. In this article, we investigate the D-optimal design problem for nonlinear quantile regression analysis. We provide a necessary condition to check the optimality of a given design and use it to determine bounds for the number of support points of locally D-optimal designs. The results are illustrated, determining locally, Bayesian and standardized maximin D-optimal designs for quantile regression analysis in the Michaelis-Menten and EMAX model, which are widely used in such important fields as toxicology, pharmacokinetics, and dose-response modeling. © 2012 American Statistical Association.

Suppose the random vector (X,Y) satisfies the regression model Y=m(X)+σ(X)e{open}, where m(ḃ) and σ(ḃ) are unknown location and scale functions and e{open} is independent of X. The response Y is subject to random right censoring, and the covariate X is completely observed. A new test for a specific parametric form of any scale function σ(ḃ) (including the standard deviation function) is proposed. Its statistic is based on the distribution of the residuals obtained from the assumed regression model. Weak convergence of the corresponding process is obtained, and its finite sample behaviour is studied via simulations. Finally, characteristics of the test are illustrated in the analysis of a fatigue data set. © 2012 Board of the Foundation of the Scandinavian Journal of Statistics.

This paper is devoted to the explicit construction of optimal designs for discrimination between two polynomial regression models of degree n - 2 and n. In a fundamental paper, Atkinson and Fedorov [Biometrika 62 (1975a) 57-70] proposed the T -optimality criterion for this purpose. Recently, Atkinson [MODA 9, Advances in Model-Oriented Design and Analysis (2010) 9-16] determined T -optimal designs for polynomials up to degree 6 numerically and based on these results he conjectured that the support points of the optimal design are cosines of the angles that divide half of the circle into equal parts if the coefficient of xn-1 in the polynomial of larger degree vanishes. In the present paper we give a strong justification of the conjecture and determine all T -optimal designs explicitly for any degree n ε ℕ. In particular, we show that there exists a one-dimensional class of T -optimal designs. Moreover, we also present a generalization to the case when the ratio between the coefficients of xn-1 and xn is smaller than a certain critical value. Because of the complexity of the optimization problem, T -optimal designs have only been determined numerically so far, and this paper provides the first explicit solution of the T -optimal design problem since its introduction by Atkinson and Fedorov [Biometrika 62 (1975a) 57-70]. Finally, for the remaining cases (where the ratio of coefficients is larger than the critical value), we propose a numerical procedure to calculate the T -optimal designs. The results are also illustrated in an example. © Institute of Mathematical Statistics, 2012.

In the common nonparametric regression model, we consider the problem of testing the hypothesis that the coefficient of the scale and location function is constant. The test is based on a comparison of the standardized (by a local linear estimate of the scale function) observations with their mean. We show weak convergence of a centered version of this process to a Gaussian process under the null hypothesis and the alternative and use this result to construct a test for the hypothesis of a constant coefficient of variation in the nonparametric regression model. A small simulation study is also presented to investigate the finite sample properties of the new test. © 2011 The Institute of Statistical Mathematics, Tokyo.

In this paper we discuss the asymptotic properties of quantile processes under random censoring. In contrast to most work in this area we prove weak convergence of an appropriately standardized quantile process under the assumption that the quantile regression model is only linear in the region, where the process is investigated. Additionally, we also discuss properties of the quantile process in sparse regression models including quantile processes obtained from the Lasso and adaptive Lasso. The results are derived by a combination of modern empirical process theory, classical martingale methods and a recent result of Kato (2009). © 2012 Allerton Press, Inc.

Ratio asymptotics for matrix orthogonal polynomials with recurrence coefficients An and Bn having limits A and B, respectively, (the matrix Nevai class) were obtained by Durán. In the present paper, we obtain an alternative description of the limiting ratio. We generalize it to recurrence coefficients which are asymptotically periodic with higher periodicity, and/or which are slowly varying as a function of a parameter. Under such assumptions, we also find the limiting zero distribution of the matrix orthogonal polynomials, thus generalizing results by Durán-López-Saff and Dette-Reuther to the non-Hermitian case. Our proofs are based on "normal family" arguments and on the solution of a quadratic eigenvalue problem. As an application of our results, we obtain new explicit formulas for the spectral measures of the matrix Chebyshev polynomials of the first and second kind and derive the asymptotic eigenvalue distribution for a class of random band matrices which generalize the tridiagonal matrices introduced by Dumitriu-Edelman. © 2012 Hebrew University Magnes Press.

We consider the problem of optimal design of experiments for random-effects models, especially population models, where a small number of correlated observations can be taken on each individual, whereas the observations corresponding to different individuals are assumed to be uncorrelated. We focus on c-optimal design problems and show that the classical equivalence theorem and the famous geometric characterization of Elfving from the case of uncorrelated data can be adapted to the problem of selecting optimal sets of observations for the n individual patients. The theory is demonstrated by finding optimal designs for a linear model with correlated observations and a non-linear random-effects population model, which is commonly used in pharmaco-kinetics. © 2010 Royal Statistical Society.

In this article we investigate the problem of measuring deviations from stationarity in locally stationary time series. Our approach is based on a direct estimate of the L 2-distance between the spectral density of the locally stationary process and its best approximation by a spectral density of a stationary process. An explicit expression of the minimal distance is derived, which depends only on integrals of the spectral density of the locally stationary process and its square. These integrals can be estimated directly without estimating the spectral density, and as a consequence, the estimation of the measure of stationarity does not require the specification of a smoothing bandwidth. We show weak convergence of an appropriately standardized version of the statistic to a standard normal distribution. The results are used to construct confidence intervals for the measure of stationarity and to develop a new test for the hypothesis of stationarity. Finally, we investigate the finite sample properties of the resulting confidence intervals and tests by means of a simulation study and illustrate the methodology in two data examples. Parts of the proofs are available online as supplemental material to this article. © 2011 American Statistical Association.

The celebrated de la Garza phenomenon states that for a polynomial regression model of degree p - 1 any optimal design can be based on at most p design points. In a remarkable paper, Yang [Ann. Statist. 38 (2010) 2499 - 2524] showed that this phenomenon exists in many locally optimal design problems for nonlinear models. In the present note, we present a different view point on these findings using results about moment theory and Chebyshev systems. In particular, we show that this phenomenon occurs in an even larger class of models than considered so far.

We consider the problem of testing the equality of J quantile curves from independent samples. A test statistic based on an L2-distance between non-crossing non-parametric estimates of the quantile curves from the individual samples is proposed. Asymptotic normality of this statistic is established under the null hypothesis, local and fixed alternatives, and the finite sample properties of a bootstrap-based version of this test statistic are investigated by means of a simulation study. © 2010 Board of the Foundation of the Scandinavian Journal of Statistics.

We consider the nonparametric estimation problem of conditional regression quantileswith high-dimensional covariates. For the additive quantile regression model, we propose a new procedure such that the estimated marginal effects of additive conditional quantile curves do not cross. The method is based on a combination of the marginal integration technique and non-increasing rearrangements, which were recently introduced in the context of estimating a monotone regression function. Asymptotic normality of the estimates is established with a one-dimensional rate of convergence and the finite sample properties are studied by means of a simulation study and a data example. © 2009 The Institute of Statistical Mathematics, Tokyo.

We propose a new class of estimators for Pickands dependence function which is based on the concept of minimum distance estimation. An explicit integral representation of the function A * (t), which minimizes a weighted L 2-distance between the logarithm of the copula C(y 1?t, y t ) and functions of the form A(t) log(y) is derived. If the unknown copula is an extreme-value copula, the function A * (t) coincides with Pickands dependence function. Moreover, even if this is not the case, the function A * (t) always satisfies the boundary conditions of a Pickands dependence function. The estimators are obtained by replacing the unknown copula by its empirical counterpart and weak convergence of the corresponding process is shown. A comparison with the commonly used estimators is performed from a theoretical point of view and by means of a simulation study. Our asymptotic and numerical results indicate that some of the new estimators outperform the estimators, which were recently proposed by Genest and Segers [Ann. Statist. 37 (2009) 2990-3022]. As a by-product of our results, we obtain a simple test for the hypothesis of an extreme-value copula, which is consistent against all positive quadrant dependent alternatives satisfying weak differentiability assumptions of first order. © Institute of Mathematical Statistics, 2011.

We consider the problem of testing parametric assumptions in an inverse regression model with a convolution-type operator. An L2-type goodness-of-fit test is proposed which compares the distance between a parametric and a nonparametric estimate of the regression function. A procedure of bootstrapping the proposed test statistic to obtain suitable approximations of critical values, along with some ideas to prove its consistency, are given. © 2011 American Institute of Physics.

We develop optimal design theory for additive partially nonlinear regression models, showing that Bayesian and standardized maximin D-optimal designs can be found as the products of the corresponding optimal designs in one dimension. A sufficient condition under which analogous results hold for Ds-optimality is derived to accommodate situations in which only a subset of the model parameters is of interest. To facilitate prediction of the response at unobserved locations, we prove similar results for Q-optimality in the class of all product designs. The usefulness of this approach is demonstrated through an application from the automotive industry, where optimal designs for least squares regression splines are determined and compared with designs commonly used in practice. © 2011 Biometrika Trust.

In the common nonparametric regression model we consider the problem of constructing optimal designs, if the unknown curve is estimated by a smoothing spline. A special basis for the space of natural splines is introduced and the local minimax property for these splines is used to derive two optimality criteria for the construction of optimal designs. The first criterion determines the design for a most precise estimation of the coefficients in the spline representation and corresponds to D-optimality, while the second criterion is the G-optimality criterion and corresponds to an accurate prediction of the curve. Several properties of the optimal designs are derived. In general, D- and G-optimal designs are not equivalent. Optimal designs are determined numerically and compared with the uniform design. © The Institute of Statistical Mathematics, Tokyo 2009.

We consider the problem of estimating the derivative of the expected response in nonlinear regression models. It is demonstrated that in many cases the optimal designs for estimating the derivative have either on m or m ? 1 support points, where m denotes the number of unknown parameters in the model. It is also shown that the support points and weights of the optimal designs are analytic functions, and this result is used to construct a numerical procedure for the calculation of the optimal designs. The results are illustrated in exponential regression and rational regression models.

In many real life applications, it is impossible to observe the feature of interest directly. For example, non-invasive medical imaging techniques rely on indirect observations to reconstruct an image of the patient's internal organs. In this paper, we investigate optimal designs for such indirect regression problems. We use the optimal designs as benchmarks to investigate the efficiency of designs commonly used in applications. Several examples are discussed for illustration. Our designs provide guidelines to scientists regarding the experimental conditions at which the indirect observations should be taken in order to obtain an accurate estimate for the object of interest. Moreover, we demonstrate that in many cases the commonly used uniform design is close to optimal. © 2011 IOP Publishing Ltd.

In the common Fourier regression model we investigate the optimal design problem for the estimation of linear combinations of the coefficients, where the explanatory variable varies in the interval [-π,π]. In a recent paper Dette et al. (2009) determined optimal designs for estimating certain pairs of the coefficients in the model. The optimal design problem corresponds to a linear optimality criterion for a specific matrix L. In the present paper these results are extended to more general matrices L. By our results the optimal design problem for a Fourier regression of large degree can be reduced to a design problem in a model of lower degree, which allows the determination of L-optimal designs in many important cases. The results are illustrated by several examples. © 2010 Elsevier B.V.

Hormesis is a widely observed phenomenon in many branches of life sciences, ranging from toxicology studies to agronomy, with obvious public health and risk assessment implications. We address optimal experimental design strategies for determining the presence of hormesis in a controlled environment using the recently proposed Hunt-Bowman model. We propose alternative models that have an implicit hormetic threshold, discuss their advantages over current models, and construct and study properties of optimal designs for (i) estimating model parameters, (ii) estimating the threshold dose, and (iii) testing for the presence of hormesis. We also determine maximin optimal designs that maximize the minimum of the design efficiencies when we have multiple design criteria or there is model uncertainty where we have a few plausible models of interest. We apply these optimal design strategies to a teratology study and show that the proposed designs outperform the implemented design by a wide margin for many situations. © 2011 Society for Risk Analysis.

Dose-finding studies are frequently conducted to evaluate the effect of different doses or concentration levels of a compound on a response of interest. Applications include the investigation of a new medicinal drug, a herbicide or fertilizer, a molecular entity, an environmental toxin, or an industrial chemical. In pharmaceutical drug development, dose-finding studies are of critical importance because of regulatory requirements that marketed doses are safe and provide clinically relevant efficacy. Motivated by a dose-finding study in moderate persistent asthma, we propose response-adaptive designs addressing two major challenges in dose-finding studies: uncertainty about the dose-response models and large variability in parameter estimates. To allocate new cohorts of patients in an ongoing study, we use optimal designs that are robust under model uncertainty. In addition, we use a Bayesian shrinkage approach to stabilize the parameter estimates over the successive interim analyses used in the adaptations. This approach allows us to calculate updated parameter estimates and model probabilities that can then be used to calculate the optimal design for subsequent cohorts. The resulting designs are hence robust with respect to model misspecification and additionally can efficiently adapt to the information accrued in an ongoing study. We focus on adaptive designs for estimating the minimum effective dose, although alternative optimality criteria or mixtures thereof could be used, enabling the design to address multiple objectives. In an extensive simulation study, we investigate the operating characteristics of the proposed methods under a variety of scenarios discussed by the clinical team to design the aforementioned clinical study. © 2013 Institute of Mathematical Statistics.

In the functional regression model where the responses are curves, new tests for the functional form of the regression and the variance function are proposed, which are based on a stochastic process estimating L2-distances. Our approach avoids the explicit estimation of the functional regression and it is shown that normalized versions of the proposed test statistics converge weakly. The finite sample properties of the tests are illustrated by means of a small simulation study. It is also demonstrated that for small samples, bootstrap versions of the tests improve the quality of the approximation of the nominal level. © 2011 Elsevier Inc.

In this article, new tests for non-parametric hypotheses in stationary processes are proposed. Our approach is based on an estimate of the L2-distance between the spectral density matrix and its best approximation under the null hypothesis. We explain the main idea in the problem of testing for a constant spectral density matrix and in the problem of comparing the spectral densities of several correlated stationary time series. The method is based on direct estimation of integrals of the spectral density matrix and does not require the specification of smoothing parameters. We show that the limit distribution of the proposed test statistic is normal and investigate the finite sample properties of the resulting tests by means of a small simulation study. © 2010 Blackwell Publishing Ltd.

We propose a test for symmetry of a regression function with a bivariate predictor based on the L2 distance between the original function and its reflection. This distance is estimated by kernel methods and it is shown that under the null hypothesis as well as under the alternative the test statistic is asymptotically normally distributed. The finite sample properties of a bootstrap version of this test are investigated by means of a simulation study and a possible application in detecting asymmetries in grey-scale images is discussed. © American Statistical Association and Taylor & Francis 2011.

To estimate the effective dose level EDα in the common binary response model, several parametric and nonparametric estimators have been proposed in the literature. In the present article, we focus on nonpara-metric methods and present a detailed numerical comparison of four different approaches to estimate the EDα nonparametrically. The methods are briefly reviewed and their finite sample properties are studied by means of a detailed simulation study. Moreover, a data example is presented to illustrate the different concepts. © 2010 Taylor & Francis.

We study the D-optimal design problem for the common weighted univariate polynomial regression model with efficiency function λ. We characterize the efficiency functions for which an explicit solution of the D-optimal design problem is available based on a differential equation for the logarithmic derivative of the efficiency function. In contrast to the common approach which starts with a given efficiency function and derives a differential equation for the supporting polynomial of the D-optimal design, we derive a differential equation for the efficiency function, such that an explicit solution of the D-optimal design problem is possible. The approach is illustrated for various convex design spaces and is depicted in several new examples. Also, this concept incorporates all classical efficiency functions discussed in the literature so far. © 2009 The Korean Statistical Society.

We consider the problem of designing experiments for regression in the presence of correlated observations with the location model as the main example. For a fixed correlation structure approximate optimal designs are determined explicitly, and it is demonstrated that under the model assumptions made by Bickel and Herzberg (1979) for the determination of asymptotic optimal design, the designs derived in this article converge weakly to the measures obtained by these authors. We also compare the asymptotic optimal design concepts of Sacks and Ylvisaker (1966, 1968) and Bickel and Herzberg (1979) and point out some inconsistencies of the latter. Finally, we combine the best features of both concepts to develop a new approach for the design of experiments for correlated observations, and it is demonstrated that the resulting design problems are related to the (logarithmic) potential theory. © 2010 American Statistical Association.

If a model is fitted to empirical data, bias can arise from terms which are not incorporated in the model assumptions. As a consequence the commonly used optimality criteria based on the generalized variance of the estimator of the model parameters may not lead to efficient designs for the statistical analysis. In this note some general aspects of all-bias designs are presented, which were introduced in this context by Box and Draper (1959). Using an interesting correspondence between the points of all-bias designs and the knots of quadrature formulas we establish sufficient conditions such that a given design is an all-bias design. The results are illustrated in the special case of spline regression models. In particular our results generalize recent findings of Woods and Lewis (2006). © 2010 Elsevier B.V. All rights reserved.

It is well known that the empirical copula process converges weakly to a centered Gaussian field. Because the covariance structure of the limiting process depends on the partial derivatives of the unknown copula several bootstrap approximations for the empirical copula process have been proposed in the literature. We present a brief review of these procedures. Because some of these procedures also require the estimation of the derivatives of the unknown copula we propose an alternative approach which circumvents this problem. Finally a simulation study is presented in order to compare the different bootstrap approximations for the empirical copula process. © 2010 Elsevier B.V.

We consider a nonparametric location scale model and propose a new test for homoscedasticity (constant scale function). The test is based on an estimate of a deterministic function that vanishes if and only if the hypothesis of a constant scale function is satisfied and an empirical process estimating this function is investigated. Weak convergence to a scaled Brownian bridge is established, which allows a simple calculation of critical values. The new test can detect alternatives converging to the null hypothesis at a rate n-1/2 and is robust with respect to the presence of outliers. The finite sample properties are investigated by means of a simulation study, and the test is compared with some nonrobust tests for a constant scale function, which have recently been proposed in the literature. © American Statistical Association and Taylor & Francis 2010.

The Michaelis-Menten model has and continues to be one of the most widely used models in many diverse fields. In the biomedical sciences, the model continues to be ubiquitous in biochemistry, enzyme kinetics studies, nutrition science, and in the pharmaceutical sciences. Despite its wide-ranging applications across disciplines, design issues for this model are given short shrift. This article focuses on design issues and provides a variety of optimal designs of this model. In addition, we evaluate robustness properties of the optimal designs under a variation in optimality criteria. To facilitate use of optimal design ideas in practice, we design a web site for generating and comparing different types of tailor-made optimal designs and user-supplied designs for the Michaelis-Menten and related models.

Space filling designs, which satisfy a uniformity property, are widely used in computer experiments. In the present paper, the performance of nonuniform experimental designs, which locate more points in a neighborhood of the boundary of the design space, is investigated. These designs are obtained by a quantile transformation of the one-dimensional projections of commonly used space-filling designs. This transformation is motivated by logarithmic potential theory, which yields the arc-sine measure as an equilibrium distribution. The methodology is illustrated for maximin Latin hypercube designs by several examples. In particular, it is demonstrated that the new designs yield a smaller integrated mean squared error for prediction.

We study the moment space corresponding to matrix measures on the unit circle. Moment points are characterized by non-negative definiteness of block Toeplitz matrices. This characterization is used to derive an explicit representation of orthogonal polynomials with respect to matrix measures on the unit circle and to present a geometric definition of canonical moments. It is demonstrated that these geometrically defined quantities coincide with the Verblunsky coefficients, which appear in the Szegö recursions for the matrix orthogonal polynomials. Finally, we provide an alternative proof of the Geronimus relations which is based on a simple relation between canonical moments of matrix measures on the interval [-1, 1] and the Verblunsky coefficients corresponding to matrix measures on the unit circle. © 2009 Elsevier Inc. All rights reserved.

An important problem in the analysis of computer experiments is the specification of the uncertainty of the prediction according to a meta-model. The Bayesian approach, developed for the uncertainty analysis of deterministic computer models, expresses uncertainty by the use of a Gaussian process. There are several versions of the Bayesian approach, which are different in many regards but all of them lead to time consuming computations for large data sets.In the present paper we introduce a new approach in which the distribution of uncertainty is obtained in a general nonparametric form. The proposed approach is called non-parametric uncertainty analysis (NPUA), which is computationally simple since it combines generic sampling and regression techniques. We compare NPUA with the Bayesian and Kriging approaches and show the advantages of NPUA for finding points for the next runs by reanalyzing the ASET model. © 2010 Elsevier B.V.

We consider design issues for toxicology studies when we have a continuous response and the true mean response is only known to be a member of a class of nested models. This class of non-linear models was proposed by toxicologists who were concerned only with estimation problems. We develop robust and efficient designs for model discrimination and for estimating parameters in the selected model at the same time. In particular, we propose designs that maximize the minimum of D- or D1-efficiencies over all models in the given class.We show that our optimal designs are efficient for determining an appropriate model from the postulated class, quite efficient for estimating model parameters in the identified model and also robust with respect to model misspecification. To facilitate the use of optimal design ideas in practice, we have also constructed a website that freely enables practitioners to generate a variety of optimal designs for a range of models and also enables them to evaluate the efficiency of any design.

In the common linear model with quantitative predictors we consider the problem of designing experiments for estimating the slope of the expected response in a regression.We discuss locally optimal designs, where the experimenter is only interested in the slope at a particular point, and standardized minimax optimal designs, which could be used if precise estimation of the slope over a given region is required. General results on the number of support points of locally optimal designs are derived if the regression functions form a Chebyshev system. For polynomial regression and Fourier regression models of arbitrary degree the optimal designs for estimating the slope of the regression are determined explicitly for many cases of practical interest. © 2010 Taylor & Francis.

We consider the problem of constructing optimal designs for population pharmacokinetics which use random effect models. It is common practice in the design of experiments in such studies to assume uncorrelated errors for each subject. In the present paper a new approach is introduced to determine efficient designs for nonlinear least squares estimation which addresses the problem of correlation between observations corresponding to the same subject. We use asymptotic arguments to derive optimal design densities, and the designs for finite sample sizes are constructed from the quantiles of the corresponding optimal distribution function. It is demonstrated that compared to the optimal exact designs, whose determination is a hard numerical problem, these designs are very efficient. Alternatively, the designs derived from asymptotic theory could be used as starting designs for the numerical computation of exact optimal designs. Several examples of linear and nonlinear models are presented in order to illustrate the methodology. In particular, it is demonstrated that naively chosen equally spaced designs may lead to less accurate estimation. © Institute ol Mathematical Statistics, 2010.

We derive locally D- and EDp-optimal designs for the exponential, log-linear and three-parameter emax models. For each model the locally D- and EDp-optimal designs are supported at the same set of points, while the corresponding weights are different. This indicates that for a given model, D-optimal designs are efficient for estimating the smallest dose that achieves 100p% of the maximum effect in the observed dose range. Conversely, EDp-optimal designs also yield good D-efficiencies. We illustrate the results using several examples and demonstrate that locally D- and EDp-optimal designs for the emax, log-linear and exponential models are relatively robust with respect to misspecification of the model parameters. © 2010 Biometrika Trust.

A key objective in the clinical development of a medicinal drug is the determination of an adequate dose level and, more broadly, the characterization of its dose response relationship. If the dose is set too high, safety and tolerability problems are likely to result, while selecting too low a dose makes it difficult to establish adequate efficacy in the confirmatory phase, possibly leading to a failed program. Hence, dose finding studies are of critical importance in drug development and need to be planned carefully. In this paper, we focus on practical considerations for establishing efficient study designs to estimate relevant target doses. We consider optimal designs for estimating both the minimum effective dose and the dose achieving a certain percentage of the maximum treatment effect. These designs are compared with D-optimal designs for a given dose response model. Extensions to robust designs accounting for model uncertainty are also discussed. A case study is used to motivate and illustrate the methods from this paper. Copyright © 2010 John Wiley & Sons, Ltd.

In this paper we consider random block matrices, which generalize the general beta ensembles recently investigated by Dumitriu and Edelmann (J. Math. Phys. 43:5830-5847, 2002; Ann. Inst. Poincaré Probab. Stat. 41:1083-1099, 2005). We demonstrate that the eigenvalues of these random matrices can be uniformly approximated by roots of matrix orthogonal polynomials which were investigated independently from the random matrix literature. As a consequence, we derive the asymptotic spectral distribution of these matrices. The limit distribution has a density which can be represented as the trace of an integral of densities of matrix measures corresponding to the Chebyshev matrix polynomials of the first kind. Our results establish a new relation between the theory of random block matrices and the field of matrix orthogonal polynomials, which have not been explored so far in the literature. © 2008 Springer Science+Business Media, LLC.

In this paper we consider random block matrices which generalize the classical Laguerre ensemble and the Jacobi ensemble. We show that the random eigenvalues of the matrices can be uniformly approximated by the zeros of matrix orthogonal polynomials and obtain a rate for the maximum difference between the eigenvalues and the zeros. This relation between the random block matrices and matrix orthogonal polynomials allows a derivation of the asymptotic spectral distribution of the matrices. © 2010 Elsevier Inc.

In a recent paper Fermanian (2005) [9] studied a goodness-of-fit test for the parametric form of a copula, which is based on an L2-distance between a parametric and a nonparametric estimate of the copula density. In the present paper we investigate the asymptotic properties of the proposed test statistic under fixed alternatives. We also study the impact of different estimates for the parameters of the finite-dimensional family of copulas specified by the null hypothesis and illustrate the performance of a parametric bootstrap procedure for the approximation of the critical values. © 2009 Elsevier Inc. All rights reserved.

We explore the relation between matrix measures and quasi-birth-and-death processes. We derive an integral representation of the transition function in terms of a matrix-valued spectral measure and corresponding orthogonal matrix polynomials. We characterize several stochastic properties of quasi-birth-and-death processes by means of this matrixmeasure and illustrate the theoretical results by several examples. Copyright © 2010 Holger Dette and Bettina Reuther.