Anytime-valid FDR control with the stopped e-BH procedure

Hongjian Wang, Sanjit Dandapanthula and Aaditya Ramdas

Statistics & Probability Letters, 2025, vol. 226, issue C

Abstract: The e-Benjamini–Hochberg (e-BH) procedure for multiple hypothesis testing is known to control the false discovery rate (FDR) under arbitrary dependence between the input e-values. This paper points out an important subtlety when applying e-BH to e-processes, the sequential counterparts of e-values: stopping multiple e-processes at a common stopping time only yields e-values if all the e-processes and the stopping time are with respect to the same global filtration. We show that this filtration issue is of real concern as e-processes are often constructed to be “local” as opposed to “global”. We formulate a condition under which these local e-processes are indeed global and thus applying e-BH to their stopped values (the “stopped e-BH procedure”) controls the FDR. The condition excludes confounding from the past and is met under most reasonable scenarios including genomics.

Keywords: Multiple testing; False discovery rate; Sequential test; e-value (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110512

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