正常分发中家庭错误率行为 (Behaviour of Familywise Error Rate in Normal Distributions)

We study the behaviour of the familywise error rate (FWER) for Bonferroni-type procedure in multiple testing problem. Das and Bhandari in a recent article have shown that, in the equicorrelated normal setup, FWER asymptotically (i.e when number of hypotheses is very large) is a convex function of correlation $\rho$ and hence an upper bound on the FWER of Bonferroni-$\alpha$ procedure is given by $\alpha(1 - \rho)$. We derive upper bounds on FWER for Bonferroni method under the equicorrelated and general normal setups in asymptotic and non-asymptotic case. We show similar results for generalized familywise error rates.

翻译：我们研究了Bonferroni型程序在多重测试问题中的家族误差率(FWER)的行为。 Das 和 Bhandari 在最近的一篇文章中表明,在与公平相关的正常设置中,FWER 的被动状态(即假设数量非常大)是相关($rho$)的共振函数,因此Bonferroni-$\alpha$程序FWER的上限由$\alpha(1 -\rho)提供。我们在与公平相关的常规设置中,在与公平性和一般的正常设置中,我们从FWER获得对Bonferroni方法的上限值,在与公平性和非补救性案例下,我们显示了对普遍家庭误差率的类似结果。