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 -family-wise error rate (kFWER, probability to make 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.
Cite
@article{arxiv.1012.4078,
title = {Type I error rate control for testing many hypotheses: a survey with proofs},
author = {Etienne Roquain},
journal= {arXiv preprint arXiv:1012.4078},
year = {2011}
}