Optimal weighting for false discovery rate control

TL;DR

This paper introduces a new step-wise procedure for controlling the false discovery rate in multiple hypothesis testing, demonstrating improved power over existing weighted methods through theoretical proofs, simulations, and genomics data application.

Contribution

It proposes a novel, more powerful FDR control procedure that outperforms existing weighted Benjamini-Hochberg methods, especially with heterogeneous p-value distributions.

Findings

The new procedure controls FDR effectively in finite samples and asymptotically.

It shows superior power compared to traditional weighted BH procedures.

Application to genomics data demonstrates practical utility.

Abstract

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.