{"ID":6621300,"CreatedAt":"2026-07-15T01:01:48.440468303Z","UpdatedAt":"2026-07-15T03:28:55.185153975Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.12208","arxiv_id":"2607.12208","title":"The Benjamini--Hochberg Procedure Can Fail to Control the FDR for Correlated Two-Sided Gaussian Tests","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 $α=0.01$, a rigorous interval-arithmetic certificate proves $FDR\u003e0.0104$ 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.","short_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 $α=0.01$, a rigorous interval-arithmetic certificate proves $FDR\u003e0.0104$ for all sufficiently large numbers...","url_abs":"https://arxiv.org/abs/2607.12208","url_pdf":"https://arxiv.org/pdf/2607.12208v1","authors":"[\"Edgar Dobriban\"]","published":"2026-07-13T23:18:13Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"cs.AI\",\"stat.ME\"]","methods":"[]","has_code":false}