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Generalized Schott type tests for complete independence in high dimensions
Journal of Multivariate Analysis ( IF 1.6 ) Pub Date : 2021-02-05 , DOI: 10.1016/j.jmva.2021.104731
Daojiang He , Huanyu Liu , Kai Xu , Mingxiang Cao

In the high dimensional setting, this article explores the problem of testing the complete independence of random variables having a multivariate normal distribution. A natural high-dimensional extension of the test in Schott (2005) is proposed for this purpose. The newly defined tests are asymptotically distribution-free as both the sample size and the number of variables go to infinity and hence have well-known critical values, accommodate situations where the number of variables is not small relative to the sample size and are applicable without specifying an explicit relationship between the number of variables and the sample size. In practice, as the true alternative hypothesis is unknown, it is unclear how to choose a powerful test. For this, we further propose an adaptive test that maintains high power across a wide range of situations. An extensive simulation study shows that the newly proposed tests are comparable to, and in many cases more powerful than, existing tests currently in the literature.



中文翻译:

全面的Schott型式测试可确保高维完全独立

在高维环境中,本文探讨了测试具有多元正态分布的随机变量的完全独立性的问题。为此,在Schott(2005)中提出了测试的自然高维扩展。新定义的测试是渐近无分布的,因为样本数量和变量数量都达到无穷大,因此具有众所周知的临界值,可以适应变量数量相对于样本数量不小的情况,并且适用于指定变量数量和样本数量之间的明确关系。在实践中,由于真正的替代假设是未知的,因此不清楚如何选择功能强大的检验。为此,我们进一步提出了一种自适应测试,可以在各种情况下保持高功率。

更新日期:2021-02-15
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