Open Access
June 2009 On a generalized false discovery rate
Sanat K. Sarkar, Wenge Guo
Ann. Statist. 37(3): 1545-1565 (June 2009). DOI: 10.1214/08-AOS617


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≥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.


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Sanat K. Sarkar. Wenge Guo. "On a generalized false discovery rate." Ann. Statist. 37 (3) 1545 - 1565, June 2009.


Published: June 2009
First available in Project Euclid: 10 April 2009

zbMATH: 1161.62041
MathSciNet: MR2509083
Digital Object Identifier: 10.1214/08-AOS617

Primary: 62J15
Secondary: 62H99

Keywords: Average power , gene expression , generalized FDR , generalized FWER , multiple hypothesis testing , oracle k-FDR procedure , stepup procedures

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 3 • June 2009
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