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On the Convergence of the Benjamini–Hochberg Procedure

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  • Dean Palejev

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
    Big Data for Smart Society (GATE) Institute, Sofia University “St. Kliment Ohridski”, 1113 Sofia, Bulgaria)

  • Mladen Savov

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
    Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, 1164 Sofia, Bulgaria)

Abstract

The Benjamini–Hochberg procedure is one of the most used scientific methods up to date. It is widely used in the field of genetics and other areas where the problem of multiple comparison arises frequently. In this paper we show that under fairly general assumptions for the distribution of the test statistic under the alternative hypothesis, when increasing the number of tests, the power of the Benjamini–Hochberg procedure has an exponential type of asymptotic convergence to a previously shown limit of the power. We give a theoretical lower bound for the probability that for a fixed number of tests the power is within a given interval around its limit together with a software routine that calculates these values. This result is important when planning costly experiments and estimating the achieved power after performing them.

Suggested Citation

  • Dean Palejev & Mladen Savov, 2021. "On the Convergence of the Benjamini–Hochberg Procedure," Mathematics, MDPI, vol. 9(17), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2154-:d:628663
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    References listed on IDEAS

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