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Title: Post-selection inference via multiple testing Authors:  Gilles Blanchard - University of Potsdam (Germany)
Pierre Neuvial - CNRS and Toulouse Mathematics Institute (France) [presenting]
Etienne Roquain - University Pierre et Marie Curie (France)
Abstract: The objective is to devise multiple testing procedures able to provide a statistical guarantee on any candidate set of rejected hypotheses, including user-defined and/or data-driven candidate sets. We introduce a general methodology relying on the control of a multiple testing error rate that we call the joint Family-Wise Error Rate (JER). Our construction generalizes existing so-called ``post hoc'' procedures under positive dependence. We propose a generic approach to build JER-controlling procedures in the situation where the joint null distribution of the test statistics is known or can be sampled from. Our theoretical statements are supported by numerical experiments.