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On Controlling the False Discovery Rate in Multiple Testing of the Means of Correlated Normals Against Two-Sided Alternatives

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arxiv 2304.05261 v1 pith:HFBBRZNF submitted 2023-04-11 math.ST stat.TH

Sanat K. Sarkar This is my paper · ORCID
classification math.STstat.TH
keywords matrixquestionalternativesanswercovariancediscoveryfalsefollowing
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This paper revisits the following open question in simultaneous testing of multivariate normal means against two-sided alternatives: Can the method of Benjamini and Hochberg (BH, 1995) control the false discovery rate (FDR) without imposing any dependence structure on the correlations? The answer to this question is generally believed to be yes, and is conjectured so in the literature since results of numerical studies investigating the question and reported in numerous papers strongly support it. No theoretical justification of this answer has yet been put forward in the literature, as far as we know. In this paper, we offer a partial proof of this conjecture. More specifically, we consider the following two settings - (i) the covariance matrix is known and (ii) the covariance matrix is an unknown scalar multiple of a known matrix - and prove that in each of these settings a BH-type stepup method based on some weighted versions of the original z- or t-test statistics controls the FDR.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. How Much Can Gaussian Dependence Inflate the Benjamini-Hochberg Procedure's FDR?

    math.ST 2026-07 accept novelty 8.0 of 10

    No universal multiplicative FDR bound holds for Benjamini-Hochberg under Gaussian dependence: worst-case FDR/q diverges like sqrt(log(1/q)), with exact constants in natural cases.

  2. Asymptotics in Multiple Hypotheses Testing under Dependence: beyond Normality

    math.ST 2024-11 conditional novelty 6.0 of 10

    For equicorrelated test statistics with light-tailed noise, the Bonferroni family-wise error rate goes to zero as the number of hypotheses grows, generalizing a known normal result.

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