On a generalized false discovery rate

Abstract

The concept of $k$-FWER has received much attention lately as an appropriate error rate for multiple testing when one seeks to control at least $k$ false rejections, for some fixed $k\ge 1$. A less conservative notion, the $k$-FDR, has been introduced very recently by Sarkar [Ann. Statist. 34 (2006) 394--415], generalizing the false discovery rate of Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289--300]. In this article, we bring newer insight to the $k$-FDR considering a mixture model involving independent $p$-values before motivating the developments of some new procedures that control it. We prove the $k$-FDR control of the proposed methods under a slightly weaker condition than in the mixture model. We provide numerical evidence of the proposed methods' superior power performance over some $k$-FWER and $k$-FDR methods. Finally, we apply our methods to a real data set.

Published in at http://dx.doi.org/10.1214/08-AOS617 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (7)

• Generalizations of the Familywise Error Rate
• Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses
• Control of generalized error rates in multiple testing
• Stepup procedures for control of generalizations of the familywise error rate
• False discovery and false nondiscovery rates in single-step multiple testing procedures
• Stepup procedures controlling generalized FWER and generalized FDR
• Generalizing Simes' test and Hochberg's stepup procedure

Cited by in corpus (5)

• On the Simes inequality and its generalization
• Private False Discovery Rate Control
• Differentially Private False Discovery Rate Control
• A New Approach for Large Scale Multiple Testing with Application to FDR Control for Graphically Structured Hypotheses
• A New Step-down Procedure for Simultaneous Hypothesis Testing Under Dependence