PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Two simple sufficient conditions for FDR control
Gilles Blanchard and Etienne Roquain
Electronic Journal of Statistics Volume 2, pp. 963-992, 2008. ISSN 1935-7524


We show that the control of the false discovery rate (FDR) for a multiple testing procedure is implied by two coupled simple sufficient conditions. The first one, which we call “self-consistency condition”, concerns the algorithm itself, and the second, called “dependency control condition” is related to the dependency assumptions on the p-value family. Many standard multiple testing procedures are self-consistent (e.g. step-up, step-down or step-up-down procedures), and we prove that the dependency control condition can be fulfilled when choosing correspondingly appropriate rejection functions, in three classical types of dependency: independence, pos- itive dependency (PRDS) and unspecified dependency. As a consequence, we recover earlier results through simple and unifying proofs while extend- ing their scope to several regards: weighted FDR, p-value reweighting, new family of step-up procedures under unspecified p-value dependency and adaptive step-up procedures. We give additional examples of other possible applications. This framework also allows for defining and studying FDR control for multiple testing procedures over a continuous, uncountable space of hypotheses.

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EPrint Type:Article
Additional Information:Published journal version based on the technical report "self-consistent multiple testing procedures"
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:4407
Deposited By:Gilles Blanchard
Deposited On:13 March 2009