Tiny but uniform improvements of adaptive BH procedures via compound e-values

TL;DR

This paper demonstrates that many adaptive FDR procedures are special cases of the e-weighted BH method and provides uniform improvements that are simple, free, and unify existing approaches, along with a new finite-sample FDR control method.

Contribution

It reveals that most adaptive FDR procedures are compound e-value-based, offers uniform improvements, and introduces a new finite-sample FDR control method for t-tests.

Findings

Most existing procedures are inadmissible and can be uniformly improved.

Improvements are small but achieved without additional assumptions.

A new method with finite-sample FDR control for t-tests is proposed.

Abstract

After the seminal Benjamini-Hochberg (BH) procedure for controlling the false discovery rate (FDR) was proposed, dozens of papers have attempted to improve its power by adapting to the unknown proportion of nulls. We observe that most null proportion estimates are simply compound e-values in disguise, and thus most adaptive FDR procedures can be interpreted as instances of the e-weighted BH (ep-BH) procedure of Ignatiadis, Wang, and Ramdas [2024], i.e., the BH procedure weighted by compound e-values. This lens helps us show that most existing procedures are inadmissible, and we provide uniform improvements to them. While the improvements are small in practice, they still come for free (without additional assumptions), and help unify the literature. We also use our "leave-one-out ep-BH method" to design a new method with finite-sample FDR control for the simultaneous t-test setting.