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Universal Multiplicative FDR Bound for Benjamini-Hochberg

Probability & statistics · posed by folklore in the FDR literature · disproved

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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).

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  1. construction · #1

    Lihua Lei, using GPT-5.6 Sol

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