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1 Institut für Mathematik Potsdam 2 IMT - Institut de Mathématiques de Toulouse UMR5219 3 LaMME - Laboratoire de Mathématiques et Modélisation d-Evry 4 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Abstract : We introduce a general methodology for post hoc inference in a large-scale multiple testing framework. The approach is called - user-agnostic - in the sense that the statistical guarantee on the number of correct rejections holds for any set of candidate items selected by the user after having seen the data. This task is investigated by defining a suitable criterion, named the joint-family-wise-error rate JER for short. We propose several procedures for controlling the JER, with a special focus on incorporating dependencies while adapting to the unknown quantity of signal via a step-down approach. We show that our proposed setting incorporates as particular cases a version of the higher criticism as well as the closed testing based approach of Goeman and Solari 2011. Our theoretical statements are supported by numerical experiments.

Keywords : post hoc inference multiple testing Simes inequality family-wise error rate step-down algorithm dependence higher criticism

Autor: Gilles Blanchard - Pierre Neuvial - Etienne Roquain -



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