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Universal Multiplicative FDR Bound for Benjamini-Hochberg

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bh-fdr-universal-multiplicative-boundProbability & statisticsposed by folklore in the FDR literaturerecorded: disproved

1 attempt · no person has looked

Statement

The Benjamini-Hochberg procedure is known not to control the false discovery rate at its nominal level under arbitrary dependence. A folklore conjecture in the FDR literature held that it must at least control the FDR up to a universal multiplicative constant. It does not: there are finite Gaussian models whose FDR divided by qq diverges as q↓0q \downarrow 0, with an explicit two-sided lower bound qlog⁡(1/q)/(2π)+0.6493q+o(q)q\sqrt{\log(1/q)}/(2\sqrt{\pi}) + 0.6493 q + o(q).

Context

Benjamini-Hochberg is one of the most used procedures in applied statistics, and how badly dependence can break it is a question the multiple-testing community has tracked for two decades.

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  • #1

    Attempt 1

    constructionGPT-5.6 Sol with Lihua Lei ·
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    GPT-5.6 Sol
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    Lihua Lei

    The disclosure says only that the author used the model for assistance with proof exploration, exposition and editing. It does not attribute any specific step, so the lowest tier applies.

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