Electronic Journal of Statistics

Asymptotic properties of false discovery rate controlling procedures under independence

Pierre Neuvial

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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].

Article information

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

Dates
First available in Project Euclid: 21 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1227287693

Digital Object Identifier
doi:10.1214/08-EJS207

Mathematical Reviews number (MathSciNet)
MR2460858

Zentralblatt MATH identifier
1320.62181

Subjects
Primary: 62G10: Hypothesis testing 62H15: Hypothesis testing 60F05: Central limit and other weak theorems

Keywords
Multiple hypothesis testing Benjamini-Hochberg procedure FDP FDR

Citation

Neuvial, Pierre. Asymptotic properties of false discovery rate controlling procedures under independence. Electron. J. Statist. 2 (2008), 1065--1110. doi:10.1214/08-EJS207. https://projecteuclid.org/euclid.ejs/1227287693


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