关于F.W.E.R.的观察和罗斯福对于相关正态分布
Observation on F.W.E.R. and F.D.R. for correlated normal
摘要：
本文研究了具有等相关正态观测值的同时检验问题的Bonferroni方法的族误差率（FWER）和Benjamini-Hodgeberg方法的错误发现率（FDR）的性质.通过模拟研究，我们证明了F.W.E.R.是一个凹函数的小数目的假设和渐近成为凸函数的相关性。F.W.E.R.和罗斯福确认如果存在非负相关，则这些过程将第一类错误率控制在比期望的显著性水平小得多的比率。这证实了当存在相关性时这些流行方法的保守性质，并通过适当调整相关性提供了提高功效的范围。
英文摘要：
In this paper, we have attempted to study the behaviour of the family wise error rate (FWER) for Bonferroni's procedure and false discovery rate (FDR) of the Benjamini-Hodgeberg procedure for simultaneous testing problem with equicorrelated normal observations. By simulation study, we have shown that F.W.E.R. is a concave function for small no. of hypotheses and asymptotically becomes a convex function of the correlation. The plots of F.W.E.R. and F.D.R. confirms that if non-negative correlation is present, then these procedures control the type-I error rate at a much smaller rate than the desired level of significance. This confirms the conservative nature of these popular methods when correlation is present and provides a scope for improvement in power by appropriate adjustment for correlation.
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