发表机构
Department of Statistics and Data Science, University of Pennsylvania（统计与数据科学系，宾夕法尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究表明本杰明尼-霍奇伯格程序在相关双边高斯检验中可能无法控制FDR，构建因子模型证明在α = 0.01时FDR > 0.0104，反驳了一个二十年的猜想，蒙特卡罗实验与理论相符，证明由GPT - 5.6 Pro获得并经作者检查。
AI 中文摘要
我们表明，对于相关的双边高斯p值，本杰明尼-霍奇伯格程序可能无法将错误发现率（FDR）控制在其名义水平。我们构建了一个因子模型，在α = 0.01的水平下，严格的区间算术证明表明，对于所有足够多的假设，FDR > 0.0104。这反驳了一个二十年来被广泛认为正确的猜想。蒙特卡罗实验与理论结果一致。证明由GPT - 5.6 Pro获得并经作者仔细检查。
英文摘要
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 $FDR>0.0104$ 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.
