On strongly coherent confidence envelopes for the false discoveries
Abstract
Coherence is a long term notion in the literature of multiple testing. From FWER control multiple testing theory to confidence envelopes on the number of false positives, coherence is a desirable property for multiple testing procedures. However, we show in this article that coherence is not a sufficient property to ensure that a multiple testing procedure is nonimprovable via an interpolation mechanism. We introduce a new no- tion, the notion of strong coherence, which is a stronger property than coherence and ensures that a multiple testing procedure is nonimprovable via the interpolation mech- anisms considered in the literature. Finally, we provide a uniform improvement of the confidence envelope from Durand et al. (2020) that is computable in polynomial time and demonstrate the improvement on simulated data.
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BibTeX
@misc{perier2026strongly,
title = {{On strongly coherent confidence envelopes for the false discoveries}},
author = {Romain Périer and Gilles Blanchard and Guillermo Durand},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22601},
eprint = {2610.22601},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22601},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On strongly coherent confidence envelopes for the false discoveries
AU - Romain Périer
AU - Gilles Blanchard
AU - Guillermo Durand
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22601
UR - https://arxiv.org/abs/2610.22601
AB - Coherence is a long term notion in the literature of multiple testing. From FWER control multiple testing theory to confidence envelopes on the number of false positives, coherence is a desirable property for multiple testing procedures. However, we show in this article that coherence is not a sufficient property to ensure that a multiple testing procedure is nonimprovable via an interpolation mechanism. We introduce a new no- tion, the notion of strong coherence, which is a stronger property than coherence and ensures that a multiple testing procedure is nonimprovable via the interpolation mech- anisms considered in the literature. Finally, we provide a uniform improvement of the confidence envelope from Durand et al. (2020) that is computable in polynomial time and demonstrate the improvement on simulated data.
ER -