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arXiv · 2504.11759

Bringing closure to FDR control: beating the e-Benjamini-Hochberg procedure

Ziyu Xu·Lasse Fischer·Aaditya Ramdas
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Abstract

False discovery rate (FDR) has been a key metric for error control in multiple hypothesis testing, and many methods have developed for FDR control across a diverse cross-section of settings and applications. We develop a closure principle for all FDR controlling procedures, i.e., we provide a characterization based on e-values for all admissible FDR controlling procedures. A general version of this closure principle can recover any multiple testing error metric and allows one to choose the error metric post-hoc. We leverage this idea to formulate the closed eBH procedure, a (usually strict) improvement over the eBH procedure for FDR control when provided with e-values. This also yields a closed BY procedure that dominates the Benjamini-Yekutieli (BY) procedure for FDR control with arbitrarily dependent p-values, thus proving that the latter is inadmissibile. We demonstrate the practical performance of our new procedures in simulations.

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Ziyu Xu, Lasse Fischer, Aaditya Ramdas. 2025-04-16. Bringing closure to FDR control: beating the e-Benjamini-Hochberg procedure. https://arxiv.org/abs/2504.11759

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