Electronic Journal of Statistics

Two simple sufficient conditions for FDR control

Gilles Blanchard and Etienne Roquain

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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.

Article information

Electron. J. Statist. Volume 2 (2008), 963-992.

First available in Project Euclid: 15 October 2008

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J15: Paired and multiple comparisons
Secondary: 62G10: Hypothesis testing

False Discovery Rate multiple testing step-up step-down step-up-down weighted p-values PRDS condition


Blanchard, Gilles; Roquain, Etienne. Two simple sufficient conditions for FDR control. Electron. J. Statist. 2 (2008), 963--992. doi:10.1214/08-EJS180. https://projecteuclid.org/euclid.ejs/1224078069

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