Operating Characteristics and Extensions of the FDR Procedure

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.