Open Access
2008 Two simple sufficient conditions for FDR control
Gilles Blanchard, Etienne Roquain
Electron. J. Statist. 2: 963-992 (2008). DOI: 10.1214/08-EJS180


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, positive dependency (PRDS) and unspecified dependency. As a consequence, we recover earlier results through simple and unifying proofs while extending 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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Gilles Blanchard. Etienne Roquain. "Two simple sufficient conditions for FDR control." Electron. J. Statist. 2 963 - 992, 2008.


Published: 2008
First available in Project Euclid: 15 October 2008

zbMATH: 1320.62179
MathSciNet: MR2448601
Digital Object Identifier: 10.1214/08-EJS180

Primary: 62J15
Secondary: 62G10

Keywords: False discovery rate , multiple testing , PRDS condition , step-down , step-up , step-up-down , weighted p-values

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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