Type I error rate control for testing many hypotheses: a survey with proofs
| Autor: | Roquain, E. |
|---|---|
| Přispěvatelé: | Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), ANR-09-JCJC-0027,DETECT,DETECT: Nouvelles approches statistiques pour la vision artificielle et la bioinformatique(2009), ANR-09-JCJC-0027-01, ANR-PARCIMONIE, ANR-09-JCJC-0101-01,ANR-09-JCJC-0027-01, ANR-PARCIMONIE, ANR-09-JCJC-0101-01, Benassù, Serena |
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
FOS: Computer and information sciences
step-up [MATH.MATH-PR] Mathematics [math]/Probability [math.PR] false discovery proportion AMS 2000 subject classifications: 62J15 62G10 multiple testing family-wise error positive dependence type I error rate step-down 62J15 62G10 Methodology (stat.ME) [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] [STAT.ME]Statistics [stat]/Methodology [stat.ME] Statistics - Methodology ComputingMilieux_MISCELLANEOUS |
| Zdroj: | Journal de la Société Française de Statistique Journal de la Société Française de Statistique, 2011, 152 (2) Journal de la Société Française de Statistique, Société Française de Statistique et Société Mathématique de France, 2011, 152 (2), pp.3-38 Journal de la Société Française de Statistique, 2011, 152 (2), pp.3-38 |
| ISSN: | 1962-5197 2102-6238 |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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