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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. Dey, Monitirtha & Bhandari, Subir Kumar, 2023. "FWER goes to zero for correlated normal," Statistics & Probability Letters, Elsevier, vol. 193(C).
    2. Ruodu Wang & Aaditya Ramdas, 2022. "False discovery rate control with e‐values," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 822-852, July.
    3. Christopher R. Genovese & Kathryn Roeder & Larry Wasserman, 2006. "False discovery control with p-value weighting," Biometrika, Biometrika Trust, vol. 93(3), pages 509-524, September.
    4. 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.
    5. Gordana Derado & F. DuBois Bowman & Clinton D. Kilts, 2010. "Modeling the Spatial and Temporal Dependence in fMRI Data," Biometrics, The International Biometric Society, vol. 66(3), pages 949-957, September.
    6. Das, Nabaneet & Bhandari, Subir Kumar, 2021. "Bound on FWER for correlated normal," Statistics & Probability Letters, Elsevier, vol. 168(C).
    7. 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.
    8. Efron, Bradley, 2007. "Correlation and Large-Scale Simultaneous Significance Testing," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 93-103, March.
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