# On least favorable configurations for step-up-down tests

Abstract : This paper investigates an open issue related to false discovery rate (FDR) control of step-up-down (SUD) multiple testing procedures. It has been established in earlier literature that for this type of procedure, under some broad conditions, and in an asymptotical sense, the FDR is maximum when the signal strength under the alternative is maximum. In other words, so-called ''Dirac uniform configurations" are asymptotically {\em least favorable} in this setting. It is known that this property also holds in a non-asymptotical sense (for any finite number of hypotheses), for the two extreme versions of SUD procedures, namely step-up and step-down (with extra conditions for the step-down case). It is therefore very natural to conjecture that this non-asymptotical {\em least favorable configuration} property could more generally be true for all ''intermediate'' forms of SUD procedures. We prove that this is, somewhat surprisingly, not the case. The argument is based on the exact calculations proposed earlier by Roquain and Villers (2011), that we extend here by generalizing Steck's recursion to the case of two populations. Secondly, we quantify the magnitude of this phenomenon by providing a nonasymptotic upper-bound and explicit vanishing rates as a function of the total number of hypotheses.
Keywords :
Type de document :
Pré-publication, Document de travail
2011
Domaine :

https://hal.archives-ouvertes.fr/hal-00617089
Contributeur : Etienne Roquain <>
Soumis le : vendredi 26 août 2011 - 09:14:17
Dernière modification le : lundi 29 mai 2017 - 14:25:13
Document(s) archivé(s) le : lundi 12 novembre 2012 - 15:50:41

### Fichiers

LFC-SUD-stat-sinica.pdf
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### Identifiants

• HAL Id : hal-00617089, version 1
• ARXIV : 1108.5262

### Citation

Gilles Blanchard, Thorsten Dickhaus, Etienne Roquain, Fanny Villers. On least favorable configurations for step-up-down tests. 2011. <hal-00617089>

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