A Uniform Improvement of the Benjamini-Hochberg Procedure using e-Closure

2026-06-01

AI Summary

This study addresses the limited statistical power of existing false discovery rate (FDR) control methods in multiple hypothesis testing by proposing a unified improvement to the Benjamini–Hochberg (BH) procedure based on the e-Closure principle. The proposed method strictly controls the FDR under positive regression dependence on a subset (PRDS) while uniformly dominating the classical BH procedure in power, offering substantial gains when a large proportion of null hypotheses are false. By integrating the e-Closure framework into FDR control for the first time, this work delivers a theoretically rigorous and practically effective enhancement of the BH method, maintaining its robustness while significantly improving detection capability in high-dimensional settings.

Abstract

This paper presents closed BH, a uniform improvement of the False Discovery Rate controlling method of Benjamini and Hochberg (BH). Closed BH is valid under the same assumption of Positive Regression Dependency on a Subset (PRDS) as BH. As a uniform improvement, closed BH never rejects fewer hypotheses than BH, but it may reject quite a few more. An increase in power is observed especially when the number of false null hypotheses is large. The novel method is constructed using the e-Closure principle, a recently derived general principle for multiple testing.

Problem

• False Discovery Rate
• Benjamini-Hochberg procedure
• multiple testing
• statistical power
• PRDS

Innovation

• closed BH
• e-Closure
• False Discovery Rate
• multiple testing
• PRDS