Optimal weighting for false discovery rate control

Etienne Roquain (1) , Mark van de Wiel (2, 3)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 Department of Mathematics [Amsterdam]
3 Dep. of Epidemiology and Biostatistics

How to weigh the Benjamini-Hochberg procedure? In the context of multiple hypothesis testing, we propose a new step-wise procedure that controls the false discovery rate (FDR) and we prove it to be more powerful than any weighted Benjamini-Hochberg procedure. Both finite-sample and asymptotic results are presented. Moreover, we illustrate good performance of our procedure in simulations and a genomics application. This work is particularly useful in the case of heterogeneous $p$-value distributions.

Mots clés: power maximization.; False discovery rate; multiple testing; $p$-value weighting; power maximization

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Probabilités [math.PR]

Etienne Roquain, Mark van de Wiel. Optimal weighting for false discovery rate control. Electronic Journal of Statistics , 2009, 3, pp.678-711. ⟨10.1214/09-EJS430⟩. ⟨hal-00306219v3⟩