Open Access
2008 Asymptotic properties of false discovery rate controlling procedures under independence
Pierre Neuvial
Electron. J. Statist. 2: 1065-1110 (2008). DOI: 10.1214/08-EJS207


We investigate the performance of a family of multiple comparison procedures for strong control of the False Discovery Rate ($\mathsf{FDR}$). The $\mathsf{FDR}$ is the expected False Discovery Proportion ($\mathsf{FDP}$), that is, the expected fraction of false rejections among all rejected hypotheses. A number of refinements to the original Benjamini-Hochberg procedure [1] have been proposed, to increase power by estimating the proportion of true null hypotheses, either implicitly, leading to one-stage adaptive procedures [4, 7] or explicitly, leading to two-stage adaptive (or plug-in) procedures [2, 21].

We use a variant of the stochastic process approach proposed by Genovese and Wasserman [11] to study the fluctuations of the $\mathsf{FDP}$ achieved with each of these procedures around its expectation, for independent tested hypotheses.

We introduce a framework for the derivation of generic Central Limit Theorems for the $\mathsf{FDP}$ of these procedures, characterizing the associated regularity conditions, and comparing the asymptotic power of the various procedures. We interpret recently proposed one-stage adaptive procedures [4, 7] as fixed points in the iteration of well known two-stage adaptive procedures [2, 21].


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Pierre Neuvial. "Asymptotic properties of false discovery rate controlling procedures under independence." Electron. J. Statist. 2 1065 - 1110, 2008.


Published: 2008
First available in Project Euclid: 21 November 2008

zbMATH: 1320.62181
MathSciNet: MR2460858
Digital Object Identifier: 10.1214/08-EJS207

Primary: 60F05 , 62G10 , 62H15

Keywords: Benjamini-Hochberg procedure , FDP , FDR , multiple hypothesis testing

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

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