  We consider controlling the false discovery rate for many tests with unknown
correlation structure. Given a large number of hypotheses, false and missing
discoveries can plague an analysis. While many procedures have been proposed to
control false discovery, they either assume independent hypotheses or lack
statistical power. We propose a novel method for false discovery control using
null bootstrapping. By bootstrapping from the correlated null, we achieve
superior statistical power to existing methods and prove that the false
discovery rate is controlled. Simulated examples illustrate the efficacy of our
method over existing methods. We apply our proposed methodology to financial
asset pricing, where the goal is to determine which "factors" lead to excess
returns out of a large number of potential factors.
