The Benjamini--Hochberg Procedure Can Fail to Control the FDR for Correlated Two-Sided Gaussian Tests

arXiv:2607.12208v1 Announce Type: cross Abstract: We show that the Benjamini--Hochberg procedure can fail to control the false discovery rate (FDR) at its nominal level for correlated two-sided Gaussian p-values. We construct a factor model for which, at level alpha=0.01, a rigorous interval-arithmetic certificate proves FDR>0.0104 for all sufficiently large numbers of hypotheses. This disproves a conjecture widely believed to be true for twenty years. Monte Carlo experiments are consistent with the theoretical result. The proof was obtained by GPT-5.6 Pro and carefully checked by the author.

Source: arXiv cs.AI | 2026-07-15