New procedures for discrete tests with proven false discovery rate control

Sebastian Döhler (1) , Guillermo Durand (2) , Etienne Roquain (2)

1 University of Applied Sciences [Darmstadt]
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We consider the problem of testing simultaneously many null hypotheses when the test statistics have a discrete distribution. We present new modifications of the Benjamini-Hochberg procedure that incorporate the discrete structure of the data in an appropriate way. These new procedures are theoretically proved to control the false discovery rate (FDR) for any fixed number of null hypotheses. A strong point of our FDR controlling methodology is that it allows to incorporate at once the discreteness and the quantity of signal of the data (so called "$\pi_0$-adaptation "). Finally, the power advantage of the new methods is demonstrated by using both numerical experiments and real data sets.

Mots clés: false discovery rate; discrete hypothesis testing; type I error rate control; adaptive procedure; step-up algorithm; step-down algorithm

Domaines: Théorie [stat.TH]

Sebastian Döhler, Guillermo Durand, Etienne Roquain. New procedures for discrete tests with proven false discovery rate control. 2017. ⟨hal-01541185v1⟩