Discussion about the quality of F-ratio resampling tests for comparing variances

Pauly, Markus

doi:10.1007/s11749-010-0194-2

Cited by 22 publications

(14 citation statements)

References 16 publications

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“…(). Following the idea of Neuhaus (), Janssen (, ), Janssen and Pauls (), Neubert and Brunner (), Pauly (), Konietschke and Pauly (), Omelka and Pauly () and Chung and Romano () we must Studentize the statistic

\sqrt N {\overset{boldX}{true}}_{\cdot}^{italicπ}

. Moreover, in factorial designs we must consider its projection into the hypothesis space.…”

Section: Wald‐type Permutation Statisticmentioning

confidence: 99%

“…It is less well known that a modified permutation principle can also be applied in situations where this invariance does not hold. First ideas in this direction have been developed by Neuhaus () and Janssen () and have been further developed and generalized by Janssen and Pauls (), Neubert and Brunner (), Pauly (), Konietschke and Pauly (), Omelka and Pauly () and Chung and Romano (). However, so far such procedures have not been studied for general heteroscedastic factorial designs.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic Permutation Tests in General Factorial Designs

Pauly

Brunner

Konietschke

2014

Journal of the Royal Statistical Society Series B: Statistical Methodology

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In 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 χ 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.

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\sqrt N {\overset{boldX}{true}}_{\cdot}^{italicπ}

. Moreover, in factorial designs we must consider its projection into the hypothesis space.…”

Section: Wald‐type Permutation Statisticmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Asymptotic Permutation Tests in General Factorial Designs

Pauly

Brunner

Konietschke

2014

Journal of the Royal Statistical Society Series B: Statistical Methodology

Self Cite

110

121

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show abstract

“…Janssen (1997Janssen ( , 2005 proposes studentized permutation tests for the parametric Behrens-Fisher problem, whereas Fay and Proschan (2010) discuss test recommendations in both Behrens-Fisher problems. Moreover, Janssen (1999a,b), Pauly (2011b), Pauly (2012, 2014), Omelka and Pauly (2012), Romano (2013, 2016), as well as Pauly et al (2015) support the use of studentized permutation tests for other testing problems.…”

Section: Introductionmentioning

confidence: 94%

Permutation‐based inference for the AUC: A unified approach for continuous and discontinuous data

2016

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We 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.

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“…Thus, a ‘classical’ permutation test would fail if data are not exchangeable. Following the ideas of Neuhaus (), Janssen (, ), Neubert and Brunner (), Pauly (), Konietschke and Pauly (), Omelka and Pauly (), Chung and Romano (, ), Pauly et al . (), Pauly, Asendorf, and Konietschke (), and Smaga (), this problem can be solved by studentizing the statistic

\sqrt{N} {\overset{R}{true}}_{\cdot}^{normalπ}

.…”

Section: Wald‐type Permutation Statisticmentioning

confidence: 99%

Rank‐based permutation approaches for non‐parametric factorial designs

M¹,

Konietschke

Pauly³

2017

Brit J Math & Statis

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Inference methods for null hypotheses formulated in terms of distribution functions in general non-parametric factorial designs are studied. The methods can be applied to continuous, ordinal or even ordered categorical data in a unified way, and are based only on ranks. In this set-up Wald-type statistics and ANOVA-type statistics are the current state of the art. The first method is asymptotically exact but a rather liberal statistical testing procedure for small to moderate sample size, while the latter is only an approximation which does not possess the correct asymptotic α level under the null. To bridge these gaps, a novel permutation approach is proposed which can be seen as a flexible generalization of the Kruskal-Wallis test to all kinds of factorial designs with independent observations. It is proven that the permutation principle is asymptotically correct while keeping its finite exactness property when data are exchangeable. The results of extensive simulation studies foster these theoretical findings. A real data set exemplifies its applicability.

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Discussion about the quality of F-ratio resampling tests for comparing variances

Abstract: Heterogeneous null distributions, Permutation tests, Bootstrap tests, Power, Studentized statistics, Two-sample tests, 62G09, 62G10,

Cited by 22 publications

References 16 publications

Asymptotic Permutation Tests in General Factorial Designs

Asymptotic Permutation Tests in General Factorial Designs

Permutation‐based inference for the AUC: A unified approach for continuous and discontinuous data

Rank‐based permutation approaches for non‐parametric factorial designs

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