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FWER goes to zero for correlated normal

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  • Dey, Monitirtha
  • Bhandari, Subir Kumar

Abstract

We study the limiting behavior of Bonferroni FWER in a multiple testing problem as the number of hypotheses grows to infinity. We establish that in the equicorrelated normal setup with positive equicorrelation, Bonferroni FWER tends to zero asymptotically. We extend this result for generalized familywise error rates and to arbitrarily correlated Normal setup.

Suggested Citation

  • Dey, Monitirtha & Bhandari, Subir Kumar, 2023. "FWER goes to zero for correlated normal," Statistics & Probability Letters, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:stapro:v:193:y:2023:i:c:s0167715222002139
    DOI: 10.1016/j.spl.2022.109700
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    References listed on IDEAS

    as
    1. Das, Nabaneet & Bhandari, Subir Kumar, 2021. "Bound on FWER for correlated normal," Statistics & Probability Letters, Elsevier, vol. 168(C).
    2. Wenguang Sun & T. Tony Cai, 2009. "Large‐scale multiple testing under dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 393-424, April.
    3. Efron, Bradley, 2010. "Correlated z-Values and the Accuracy of Large-Scale Statistical Estimates," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1042-1055.
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