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Journal Articles Journal de la Société Française de Statistique Year : 2011

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

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.

#### Domains

Statistics [stat] Methodology [stat.ME]

### Dates and versions

hal-00547965 , version 1 (18-12-2010)
hal-00547965 , version 2 (14-03-2011)
hal-00547965 , version 3 (28-12-2022)

### Identifiers

• HAL Id : hal-00547965 , version 3
• ARXIV :

### Cite

Etienne Roquain. Type I error rate control for testing many hypotheses: a survey with proofs. Journal de la Société Française de Statistique, 2011, 152 (2). ⟨hal-00547965v3⟩

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