Optimal weighting for false discovery rate control

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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.