Department of Statistics Unitmark
Dietrich College of Humanities and Social Sciences

Operating Characteristics and Extensions of the FDR Procedure

Publication Date

March, 2001

Publication Type

Tech Report

Author(s)

Christopher Genovese and Larry Wasserman

Abstract

We investigate the operating characteristics of the Benjamini-Hochberg false discovery rate (FDR) procedure for multiple testing. This is a distribution free method that controls the expected fraction of falsely rejected null hypotheses among those rejected. This paper provides a framework for understanding how and why this procedure works. We start by studying the special case where the p-values under the alternative have a common distribution, where we are able to obtain many insights into this new procedure. We first obtain bounds on the "deciding point" D that determines the critical p-value. From this, we obtain explicit asymptotic expressions for a particular risk funciton. We introduce the dual notion of false non-rejections (FNR) and we consider a risk function that combines FDR and FNR. We also consider the optimal procedure with respect to a measure of conditional risk.