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Electronic Journal of Statistics

Asymptotic properties of false discovery rate controlling procedures under independence

Pierre Neuvial
Source: Electron. J. Statist. Volume 2 (2008), 1065-1110.

Abstract

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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Primary Subjects: 62G10, 62H15, 60F05
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Permanent link to this document: http://projecteuclid.org/euclid.ejs/1227287693
Digital Object Identifier: doi:10.1214/08-EJS207
Mathematical Reviews number (MathSciNet): MR2460858

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