On the Convergence of the Benjamini–Hochberg Procedure

Dean Palejev and Mladen Savov
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Dean Palejev: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
Mladen Savov: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria

Mathematics, 2021, vol. 9, issue 17, 1-19

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.

Keywords: multiple hypothesis testing; Benjamini–Hochberg procedure; convergence rate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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