Admissibility and Complete Classes for False Discovery Rate Control with E-values
Abstract
The false discovery rate (FDR) is the most widely used error metric in modern multiple testing. We provide a comprehensive analysis of the admissibility of e-value-based procedures with FDR control. We consider both simultaneous and point procedures and introduce strong and weak notions of dominance. Every simultaneous procedure is strongly, and hence weakly, dominated by an admissible weighted-mean closed e-Benjamini--Hochberg (eBH̅) procedure, and thus weighted-mean eBH̅ procedures form a complete class. Every constant-free weighted-mean eBH̅ procedure is admissible at every level, and we propose two ways for choosing constant-free weights based on side information, such as pre-screening data. Within the symmetric class, the usual mean eBH̅ procedure is the largest element if and only if the FDR level is small enough; otherwise this class has no largest element. We also obtain results on the admissibility of symmetric weighted-mean eBH̅ procedures with non-zero constant terms. Point e-testing procedures have a parallel theory of admissibility. These results highlight the central role of weighted-mean eBH̅ procedures in multiple testing.
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BibTeX
@misc{sun2026admissibility,
title = {{Admissibility and Complete Classes for False Discovery Rate Control with E-values}},
author = {Liulei Sun and Ruodu Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.14380},
eprint = {2607.14380},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.14380},
}
RIS
TY - UNPB
TI - Admissibility and Complete Classes for False Discovery Rate Control with E-values
AU - Liulei Sun
AU - Ruodu Wang
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2607.14380
UR - https://arxiv.org/abs/2607.14380
AB - The false discovery rate (FDR) is the most widely used error metric in modern multiple testing. We provide a comprehensive analysis of the admissibility of e-value-based procedures with FDR control. We consider both simultaneous and point procedures and introduce strong and weak notions of dominance. Every simultaneous procedure is strongly, and hence weakly, dominated by an admissible weighted-mean closed e-Benjamini--Hochberg (eBH̅) procedure, and thus weighted-mean eBH̅ procedures form a complete class. Every constant-free weighted-mean eBH̅ procedure is admissible at every level, and we propose two ways for choosing constant-free weights based on side information, such as pre-screening data. Within the symmetric class, the usual mean eBH̅ procedure is the largest element if and only if the FDR level is small enough; otherwise this class has no largest element. We also obtain results on the admissibility of symmetric weighted-mean eBH̅ procedures with non-zero constant terms. Point e-testing procedures have a parallel theory of admissibility. These results highlight the central role of weighted-mean eBH̅ procedures in multiple testing.
ER -