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On the Simes test under dependence

Author

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  • H. Finner

    (Leibniz Institute for Diabetes Research at Heinrich-Heine-University Düsseldorf)

  • M. Roters

    (Universität Trier)

  • K. Strassburger

    (Leibniz Institute for Diabetes Research at Heinrich-Heine-University Düsseldorf)

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.

Suggested Citation

  • H. Finner & M. Roters & K. Strassburger, 2017. "On the Simes test under dependence," Statistical Papers, Springer, vol. 58(3), pages 775-789, September.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:3:d:10.1007_s00362-015-0725-8
    DOI: 10.1007/s00362-015-0725-8
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    References listed on IDEAS

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    1. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities II. Multivariate reverse rule distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 499-516, December.
    2. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    3. Gontscharuk, Veronika & Finner, Helmut, 2013. "Asymptotic FDR control under weak dependence: A counterexample," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1888-1893.
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    Cited by:

    1. Xiong, Peihan & Hu, Taizhong, 2022. "On Samuel’s p-value model and the Simes test under dependence," Statistics & Probability Letters, Elsevier, vol. 187(C).
    2. Fengqing Zhang & Jiangtao Gou, 2021. "Refined critical boundary with enhanced statistical power for non-directional two-sided tests in group sequential designs with multiple endpoints," Statistical Papers, Springer, vol. 62(3), pages 1265-1290, June.

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