1,721,164 research outputs found
A studentized permutation test for the nonparametric Behrens-Fisher problem in paired data
No full textWe consider nonparametric ranking methods for matched pairs, whose distributions can have different shapes even under the null hypothesis of no treatment effect. Although the data may not be exchangeable under the null, we investigate a permutation approach as a valid procedure for finite sample sizes. In particular, we derive the limit of the studentized permutation distribution under alternatives, which can be used for the construction of (1 - alpha)-confidence intervals. Simulation studies show that the new approach is more accurate than its competitors. The procedures are illustrated using a real data set.German Research Foundation [DFG-Br 655/16-1, HO 1687/9-1
Permutation-based inference for the AUC: A unified approach for continuous and discontinuous data
No full textWe investigate rank-based studentized permutation methods for the nonparametric Behrens-Fisher problem, that is, inference methods for the area under the ROC curve. We hereby prove that the studentized permutation distribution of the Brunner-Munzel rank statistic is asymptotically standard normal, even under the alternative. Thus, incidentally providing the hitherto missing theoretical foundation for the Neubert and Brunner studentized permutation test. In particular, we do not only show its consistency, but also that confidence intervals for the underlying treatment effects can be computed by inverting this permutation test. In addition, we derive permutation-based range-preserving confidence intervals. Extensive simulation studies show that the permutation-based confidence intervals appear to maintain the preassigned coverage probability quite accurately (even for rather small sample sizes). For a convenient application of the proposed methods, a freely available software package for the statistical software R has been developed. A real data example illustrates the application.German Research Foundation [DFG Br 655/16-1, Ho 1687/9-1, Pa 2409/3-1
Bootstrapping and permuting paired t-test type statistics
Full text linkWe study various bootstrap and permutation methods for matched pairs, whose distributions can have different shapes even under the null hypothesis of no treatment effect. Although the data may not be exchangeable under the null, we investigate different permutation approaches as valid procedures for finite sample sizes. It will be shown that permutation or bootstrap schemes, which neglect the dependency structure in the data, are asymptotically valid. Simulation studies show that these new tests improve the power of the t-test under non-normality.German Research Foundation [DFG-Br 655/16-1, DFG-Ho 1687/9-1
Analysis of high-dimensional one group repeated measures designs
No full textWe propose a novel one sample test for repeated measures designs and derive its limit distribution for the situation where both the sample size n as well as the dimension d of the observations go to infinity. This covers the high-dimensional case with d > n. The tests are based on a quadratic form which involve new unbiased and dimension-stable estimators of different traces of the underlying unrestricted covariance structure. It is shown that the asymptotic distribution of the statistic may be standard normal, standardized chi(2)-distributed, or even of weighted chi(2)-form in some situations. To this end, we suggest an approximation technique which is asymptotically valid in the first two cases and provides an accurate approximation for the latter. We motivate and illustrate the application with a sleep lab data set and also discuss the practical meaning of d -> infinity in case of repeated measures designs. It turns out that the limit behaviour depends on how the number of repeated measures is increased which is crucial for application.German Research Foundation [DFG-PA 2409/3-1
Asymptotic permutation tests in general factorial designs
No full textIn general factorial designs where no homoscedasticity or a particular error distribution is assumed, the well-known Wald-type statistic is a simple asymptotically valid procedure. However, it is well known that it suffers from a poor finite sample approximation since the convergence to its (2) limit distribution is quite slow. This becomes even worse with an increasing number of factor levels. The aim of the paper is to improve the small sample behaviour of the Wald-type statistic, maintaining its applicability to general settings as crossed or hierarchically nested designs by applying a modified permutation approach. In particular, it is shown that this approach approximates the null distribution of the Wald-type statistic not only under the null hypothesis but also under the alternative yielding an asymptotically valid permutation test which is even finitely exact under exchangeability. Finally, its small sample behaviour is compared with competing procedures in an extensive simulation study.German Research Foundation [DFG-Br 655/16-1, Ho 1687/9-1
Permuting longitudinal data in spite of the dependencies
Full text linkFor general repeated measures designs the Wald-type statistic (WTS) is an asymptotically valid procedure allowing for unequal covariance matrices and possibly non-normal multivariate observations. The drawback of this procedure is its poor performance for small to moderate samples, i.e., decisions based on the WTS may become quite liberal. It is the aim of the present paper to improve the small-sample behavior of the WTS by means of a novel permutation procedure. In particular, it is shown that a permutation version of the WTS inherits its good large-sample properties while yielding a very accurate finite-sample control of the type-I error as shown in extensive simulations. Moreover, the new permutation method is motivated by a practical data set of a split plot design with a factorial structure on the repeated measures. (C) 2016 Elsevier Inc. All rights reserved.Deutsche Forschungsgemeinschaft [DFG-PA 2409/3-1
Robust confidence intervals for meta-regression with interaction effects
No full textAbstract Meta-analysis is an important statistical technique for synthesizing the results of multiple studies regarding the same or closely related research question. So-called meta-regression extends meta-analysis models by accounting for study-level covariates. Mixed-effects meta-regression models provide a powerful tool for evidence synthesis, by appropriately accounting for between-study heterogeneity. In fact, modelling the study effect in terms of random effects and moderators not only allows to examine the impact of the moderators, but often leads to more accurate estimates of the involved parameters. Nevertheless, due to the often small number of studies on a specific research topic, interactions are often neglected in meta-regression. In this work we consider the research questions (i) how moderator interactions influence inference in mixed-effects meta-regression models and (ii) whether some inference methods are more reliable than others. Here we review robust methods for confidence intervals in meta-regression models including interaction effects. These methods are based on the application of robust sandwich estimators of Hartung-Knapp-Sidik-Jonkman ( HKSJ ) or heteroscedasticity-consistent ( HC )-type for estimating the variance-covariance matrix of the vector of model coefficients. Furthermore, we compare different versions of these robust estimators in an extensive simulation study. We thereby investigate coverage and width of seven different confidence intervals under varying conditions. Our simulation study shows that the coverage rates as well as the interval widths of the parameter estimates are only slightly affected by adjustment of the parameters. It also turned out that using the Satterthwaite approximation for the degrees of freedom seems to be advantageous for accurate coverage rates. In addition, different to previous analyses for simpler models, the HKSJ -estimator shows a worse performance in this more complex setting compared to some of the HC -estimators.German Research Foundation 501100001659Technische Universität Dortmund 50110001637
Semi‐parametric analysis of overdispersed count and metric data with varying follow‐up times: Asymptotic theory and small sample approximations
No full textCount data are common endpoints in clinical trials, for example magnetic resonance imaging lesion counts in multiple sclerosis. They often exhibit high levels of overdispersion, that is variances are larger than the means. Inference is regularly based on negative binomial regression along with maximum-likelihood estimators. Although this approach can account for heterogeneity it postulates a common overdispersion parameter across groups. Such parametric assumptions are usually difficult to verify, especially in small trials. Therefore, novel procedures that are based on asymptotic results for newly developed rate and variance estimators are proposed in a general framework. Moreover, in case of small samples the procedures are carried out using permutation techniques. Here, the usual assumption of exchangeability under the null hypothesis is not met due to varying follow-up times and unequal overdispersion parameters. This problem is solved by the use of studentized permutations leading to valid inference methods for situations with (i) varying follow-up times, (ii) different overdispersion parameters, and (iii) small sample sizes
Wild bootstrapping rank-based procedures: Multiple testing in nonparametric factorial repeated measures designs
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