Type I error rate control for testing many hypotheses: a survey with proofs

Abstract : This paper presents a survey on some recent advances for the type I error rate control in multiple testing methodology. We consider the problem of controlling the $k$-family-wise error rate (kFWER, probability to make $k$ false discoveries or more) and the false discovery proportion (FDP, proportion of false discoveries among the discoveries). The FDP is controlled either via its expectation, which is the so-called false discovery rate (FDR), or via its upper-tail distribution function. We aim at deriving general and unified results together with concise and simple mathematical proofs. Furthermore, while this paper is mainly meant to be a survey paper, some new contributions for controlling the kFWER and the upper-tail distribution function of the FDP are provided. In particular, we derive a new procedure based on the quantiles of the binomial distribution that controls the FDP under independence.
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Contributor : Etienne Roquain <>
Submitted on : Monday, March 14, 2011 - 10:49:11 AM
Last modification on : Wednesday, May 15, 2019 - 3:32:51 AM
Long-term archiving on: Wednesday, June 15, 2011 - 2:40:57 AM


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  • HAL Id : hal-00547965, version 2
  • ARXIV : 1012.4078


Etienne Roquain. Type I error rate control for testing many hypotheses: a survey with proofs. 2011. ⟨hal-00547965v2⟩



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