Post hoc inference via joint family-wise error rate control

Gilles Blanchard (1) , Pierre Neuvial (2, 3) , Etienne Roquain (4)

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

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.

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

Domaines: Statistiques [math.ST]; Méthodologie [stat.ME]

Gilles Blanchard, Pierre Neuvial, Etienne Roquain. Post hoc inference via joint family-wise error rate control. 2017. ⟨hal-01483585v2⟩