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FWER for normal distribution in nearly independent setup

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  • Das, Nabaneet
  • Bhandari, Subir Kumar

Abstract

Das and Bhandari (2021) demonstrated that the Family-Wise Error Rate (FWER) of Bonferroni procedure is asymptotically bounded by α(1−ρ), where ρ is the correlation among hypotheses and α is the significance level. Dey and Bhandari (2023) expanded on this by showing that, under equicorrelated normal distribution, the FWER approaches zero as the number of hypotheses increases. Their findings also reveal a key insight: while the FWER stays positive when there is no correlation, it asymptotically tends to zero with any non-zero correlation, indicating a discontinuity at ρ=0. This suggests the need to investigate how the FWER behaves as correlation coefficients approach zero. This paper aims to explore how closely the FWER of Bonferroni method resembles its behavior under independence and introduces an asymptotic correction factor to improve accuracy in nearly independent cases.

Suggested Citation

  • Das, Nabaneet & Bhandari, Subir Kumar, 2025. "FWER for normal distribution in nearly independent setup," Statistics & Probability Letters, Elsevier, vol. 219(C).
    • Handle: RePEc:eee:stapro:v:219:y:2025:i:c:s0167715224003092
    DOI: 10.1016/j.spl.2024.110340
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    References listed on IDEAS

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    1. Proschan, Michael A. & Shaw, Pamela A., 2011. "Asymptotics of Bonferroni for dependent normal test statistics," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 739-748, July.
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