On the Simes inequality in elliptical models

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• 作者：Taras Bodnar ; Thorsten Dickhaus
• 关键词：Covariance matrix ; Distributional transform ; Multiple testing ; Multivariate normal distribution ; p value ; Student’s t ; Total positivity
• 刊名：Annals of the Institute of Statistical Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：69
• 期：1
• 页码：215-230
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics, general; Statistics for Business/Economics/Mathematical Finance/Insurance;
• 出版者：Springer Japan
• ISSN：1572-9052
• 卷排序：69

文摘

We provide some necessary and some sufficient conditions for the validity of the inequality of Simes in models with elliptical dependencies. Necessary conditions are presented in terms of sufficient conditions for the reverse Simes inequality. One application of our main results concerns the problem of model misspecification, in particular the case that the assumption of Gaussianity of test statistics is violated. Since our sufficient conditions require non-negativity of correlation coefficients between test statistics, we also develop two exact tests for vectors of correlation coefficients and compare their powers in computer simulations.