  How to weigh the Benjamini-Hochberg procedure? In the context of multiple
hypothesis testing, we propose a new step-wise procedure that controls the
false discovery rate (FDR) and we prove it to be more powerful than any
weighted Benjamini-Hochberg procedure. Both finite-sample and asymptotic
results are presented. Moreover, we illustrate good performance of our
procedure in simulations and a genomics application. This work is particularly
useful in the case of heterogeneous $p$-value distributions.
