On the Simes test under dependence

On the Simes test under dependence In 1986, R. J. Simes proposed a modified Bonferroni test procedure for testing an overall null hypothesis in multiple testing problems, nowadays referred to as the Simes test. The paper of Simes may be considered as a basic step in the development of many new test procedures and new error rate criteria as for example control of the false discovery rate. A key issue is the validity of the Simes test and the underlying Simes inequality under dependence. Although it has been proved that the Simes inequality is valid under suitable assumptions on dependence structures, important cases are not covered yet. In this note we investigate p-values based on exchangeable test statistics in order to explore reasons for the validity or failure of the Simes inequality. We provide sufficient conditions for the asymptotic validity of the Simes inequality and its possible strictness. We also show by means of an easy-to-compute counterexample that exchangeability by itself is not sufficient for the validity of the Simes inequality. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Statistical Papers Springer Journals

On the Simes test under dependence

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2015 by Springer-Verlag Berlin Heidelberg
Subject
Statistics; Statistics for Business/Economics/Mathematical Finance/Insurance; Probability Theory and Stochastic Processes; Economic Theory/Quantitative Economics/Mathematical Methods; Operations Research/Decision Theory
ISSN
0932-5026
eISSN
1613-9798
D.O.I.
10.1007/s00362-015-0725-8
Publisher site
See Article on Publisher Site

Abstract

In 1986, R. J. Simes proposed a modified Bonferroni test procedure for testing an overall null hypothesis in multiple testing problems, nowadays referred to as the Simes test. The paper of Simes may be considered as a basic step in the development of many new test procedures and new error rate criteria as for example control of the false discovery rate. A key issue is the validity of the Simes test and the underlying Simes inequality under dependence. Although it has been proved that the Simes inequality is valid under suitable assumptions on dependence structures, important cases are not covered yet. In this note we investigate p-values based on exchangeable test statistics in order to explore reasons for the validity or failure of the Simes inequality. We provide sufficient conditions for the asymptotic validity of the Simes inequality and its possible strictness. We also show by means of an easy-to-compute counterexample that exchangeability by itself is not sufficient for the validity of the Simes inequality.

Journal

Statistical PapersSpringer Journals

Published: Oct 31, 2015

References

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