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

초록

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.

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