mlsanityData to 14 Oct 2026

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

arXiv 2607.12208 ↗First posted 13 Jul 2026math.ST cs.AI stat.MEcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 6 of its 28 references that are in the map. First posted on arXiv 13 Jul 2026.

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References · 6

  1. 2020Conditional calibration for false discovery rate control under dependencecited by 11
  2. 2025Point Convergence of Nesterov's Accelerated Gradient Method: An AI-Assisted Proofcited by 11
  3. 2025Solving a Research Problem in Mathematical Statistics with AI Assistancecited by 6
  4. 2025G"odel Test: Can Large Language Models Solve Easy Conjectures?cited by 5
  5. 2025Accelerating mathematical research with language models: A case study of an interaction with GPT-5-Pro on a convex analysis problemcited by 5
  6. 2025Dependence-Aware False Discovery Rate Control in Two-Sided Gaussian Mean Testingcited by 1

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