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Benjamini-Hochberg FDR Under Correlated Gaussian Tests

Probability & statistics · posed by 2006 · disproved

1 attempt

Statement

Does the Benjamini-Hochberg procedure always control the false-discovery rate at its nominal level for correlated two-sided Gaussian p-values? A factor model gives FDR>0.0104\mathrm{FDR} > 0.0104 at nominal level α=0.01\alpha = 0.01.

Context

FDR under correlation is a widely felt applied-statistics question, but diffuse as a single problem.

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1 attempt

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  • #1

    Attempt 1

    constructionGPT-5.6 Pro with Edgar Dobriban ·
    AI involvement
    ai discovered
    — the result was found by a model.
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    GPT-5.6 Pro
    people
    Edgar Dobriban

    The counterexample was obtained by GPT-5.6 Pro and carefully checked by the author, with a rigorous interval-arithmetic certificate valid for all sufficiently large numbers of hypotheses.

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