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

By Etienne Roquain

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

Topics: multiple testing, type I error rate, false discovery proportion, family-wise error, step-up, step-down, positive dependence, 62J15;62G10, [ STAT.ME ] Statistics [stat]/Methodology [stat.ME]
Publisher: HAL CCSD
Year: 2011
OAI identifier: oai:HAL:hal-00547965v2
Provided by: Hal-Diderot

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