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<p>In this paper, we are interested in the limiting distribution of the number of false positives when using Bonferroni adjustment for large-scale multiple testing, as the number of hypotheses grows to infinity. It is proven in the literature that the distribution converges to a Poisson distribution, if the statistics are positively equi-correlated normal but nearly independent. In this paper, we provide an alternative proof using the Chen–Stein method. Unlike existing works, our proof provides a rate of convergence of the number of false positives to its asymptotic distribution, which we also confirm numerically. In addition, we show that our results are applicable to a more generalized setting beyond the equi-correlation assumption.</p>

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Asymptotic error of Bonferroni procedure under weak dependence via Chen–Stein method

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Kwangok Seo,
  • Seonghun Cho,
  • Johan Lim

摘要

In this paper, we are interested in the limiting distribution of the number of false positives when using Bonferroni adjustment for large-scale multiple testing, as the number of hypotheses grows to infinity. It is proven in the literature that the distribution converges to a Poisson distribution, if the statistics are positively equi-correlated normal but nearly independent. In this paper, we provide an alternative proof using the Chen–Stein method. Unlike existing works, our proof provides a rate of convergence of the number of false positives to its asymptotic distribution, which we also confirm numerically. In addition, we show that our results are applicable to a more generalized setting beyond the equi-correlation assumption.