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February 2002 Some Results on False Discovery Rate in Stepwise multiple testing procedures
Sanat K. Sarkar
Ann. Statist. 30(1): 239-257 (February 2002). DOI: 10.1214/aos/1015362192


The concept of false discovery rate (FDR) has been receiving increasing attention by researchers in multiple hypotheses testing. This paper produces some theoretical results on the FDR in the context of stepwise multiple testing procedures with dependent test statistics. It was recently shown by Benjamini and Yekutieli that the Benjamini–Hochberg step-up procedure controls the FDR when the test statistics are positively dependent in a certain sense. This paper strengthens their work by showing that the critical values of that procedure can be used in a much more general stepwise procedure under similar positive dependency. It is also shown that the FDR-controlling Benjamini–Liu step-down procedure originally developed for independent test statistics works even when the test statistics are positively dependent in some sense. An explicit expression for the FDR of a generalized stepwise procedure and an upper bound to the FDR of a step-down procedure are obtained in terms of probability distributions of ordered components of dependent random variables before establishing the main results.


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Sanat K. Sarkar. "Some Results on False Discovery Rate in Stepwise multiple testing procedures." Ann. Statist. 30 (1) 239 - 257, February 2002.


Published: February 2002
First available in Project Euclid: 5 March 2002

zbMATH: 1101.62349
MathSciNet: MR1892663
Digital Object Identifier: 10.1214/aos/1015362192

Primary: 62H15 , 62H99

Keywords: Benjamini–Liu step-down procedure , Generalized step-up–step-down procedure , multivariate totally positive of order 2 , positive regression dependency on subset

Rights: Copyright © 2002 Institute of Mathematical Statistics


Vol.30 • No. 1 • February 2002
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