737
Christopher Genovese and Larry Wasserman
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.
Keywords: Multiple Testing, p-values, Risk, False Discovery Rate