Universal Multiplicative FDR Bound for Benjamini-Hochberg

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 $q$ diverges as $q \downarrow 0$, with an explicit two-sided lower bound $q\sqrt{\log(1/q)}/(2\sqrt{\pi}) + 0.6493 q + o(q)$.

Result

Disproved

Status

Resolved

AI contribution

AI-assisted

Method

Construction

Field

Statistics

Posed by

folklore in the FDR literature

Year posed

—

Years open

—

Solved

2026-07-20

Model

GPT-5.6 Sol

Vendor

OpenAI

Collaborators

Lihua Lei

Verification

Unreviewed

Publication

Preprint

Significance

30 / 100*

Disclosed cost

—

Wikipedia

No dedicated article