New adaptive step-up procedures that control the FDR under independence and dependence

Gilles Blanchard (1) , Etienne Roquain (2)

1 Fraunhofer IAIS - Fraunhofer Institute for Intelligent Analysis and Information Systems
2 MIG - Unité Mathématique Informatique et Génome

The proportion $\pi_0$ of true null hypotheses is a quantity that often appears explicitly in the FDR control bounds. In order to obtain more powerful procedures, recent research effort has focussed on finding ways to estimate this quantity and incorporate it in a meaningful way in multiple testing procedures, leading to so-called "adaptive" procedures. We present here new adaptive multiple testing procedures with control of the false discovery rate (FDR), respectively in the independent, positive dependent and distribution-free context. In the independent context, we present a procedure that is less conservative than a recent adaptive procedure proposed by Benjamini, Krieger and Yekutieli (2006). In the positive dependence and distribution-free contexts, owing to Markov's inequality, we propose adaptive versions of the existing procedures of Benjamini and Yekutieli (2001) and Blanchard and Fleuret (2007), which present an improvment of the power when a "large" number of hypotheses are expected to be rejected.

Mots clés: multiple testing; FDR control; adaptive step-up procedures; two-stage procedures

Domaines: Statistiques [math.ST]

Gilles Blanchard, Etienne Roquain. New adaptive step-up procedures that control the FDR under independence and dependence. 2007. ⟨hal-00159723v1⟩