Interpolation and coherence in multiple testing
Abstract
In the literature on multiple testing methods that control the familywise error rate, a fundamental concept is "coherence". A procedure is coherent if it is "logically consistent" (Hochberg and Tamhane, 1987) in the sense that if a hypothesis is rejected, then all hypotheses that imply it are also rejected. If a method is not coherent, then it can be made coherent without increasing the familywise error rate. Recently, the concept of coherence was generalized to a much broader class of multiple testing procedures, namely all methods that provide simultaneous confidence bounds for false discovery proportions. Such procedures were defined to be coherent if they cannot be further improved through a process called "interpolation". However, we show that such a coherent procedure can sometimes be further improved by exploiting remaining logical inconsistencies. This leads to what we call a "perfectly coherent" method. Thus, interpolation does not necessarily lead to perfect coherence. However, we provide conditions under which it does. Fortunately, many methods based on interpolation turn out to be perfectly coherent.
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BibTeX
@misc{tran2026interpolation,
title = {{Interpolation and coherence in multiple testing}},
author = {Ninh Tran and Dennis Leung and Jesse Hemerik},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18205},
eprint = {2610.18205},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18205},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Interpolation and coherence in multiple testing
AU - Ninh Tran
AU - Dennis Leung
AU - Jesse Hemerik
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18205
UR - https://arxiv.org/abs/2610.18205
AB - In the literature on multiple testing methods that control the familywise error rate, a fundamental concept is "coherence". A procedure is coherent if it is "logically consistent" (Hochberg and Tamhane, 1987) in the sense that if a hypothesis is rejected, then all hypotheses that imply it are also rejected. If a method is not coherent, then it can be made coherent without increasing the familywise error rate. Recently, the concept of coherence was generalized to a much broader class of multiple testing procedures, namely all methods that provide simultaneous confidence bounds for false discovery proportions. Such procedures were defined to be coherent if they cannot be further improved through a process called "interpolation". However, we show that such a coherent procedure can sometimes be further improved by exploiting remaining logical inconsistencies. This leads to what we call a "perfectly coherent" method. Thus, interpolation does not necessarily lead to perfect coherence. However, we provide conditions under which it does. Fortunately, many methods based on interpolation turn out to be perfectly coherent.
ER -