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Bound on FWER for correlated normal

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  • Das, Nabaneet
  • Bhandari, Subir Kumar

Abstract

We have considered equicorrelated observations from normal distribution for simultaneous testing problem. In this article, we have shown that FWER asymptotically is a convex function of the correlation (ρ) and hence an upper bound on the FWER of Bonferroni-α procedure is α(1−ρ). This implies that Bonferroni’s method actually controls the FWER at a much smaller level than the desired level of significance under the positively correlated case and necessitates a correlation correction.

Suggested Citation

  • Das, Nabaneet & Bhandari, Subir Kumar, 2021. "Bound on FWER for correlated normal," Statistics & Probability Letters, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:stapro:v:168:y:2021:i:c:s0167715220302467
    DOI: 10.1016/j.spl.2020.108943
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. Dey, Monitirtha & Bhandari, Subir Kumar, 2023. "FWER goes to zero for correlated normal," Statistics & Probability Letters, Elsevier, vol. 193(C).

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