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On the Simes test under dependence

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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.

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Acknowledgments

This work was supported by the Ministry of Science and Research of the State of North Rhine-Westphalia (MIWF NRW) and the German Federal Ministry of Health (BMG).

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Authors and Affiliations

  1. Institute for Biometrics and Epidemiology, German Diabetes Center, Leibniz Institute for Diabetes Research at Heinrich-Heine-University Düsseldorf, Düsseldorf, Germany

    H. Finner & K. Strassburger

  2. Fachbereich IV – Mathematik, Universität Trier, Trier, Germany

    M. Roters

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  1. H. Finner
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  2. M. Roters
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  3. K. Strassburger
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Correspondence to H. Finner.

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Finner, H., Roters, M. & Strassburger, K. On the Simes test under dependence. Stat Papers 58, 775–789 (2017). https://doi.org/10.1007/s00362-015-0725-8

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  • DOI: https://doi.org/10.1007/s00362-015-0725-8

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