文章基本信息

标题：On the sphericity test with large-dimensional observations
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作者：Qinwen Wang ; Jianfeng Yao
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2013
卷号：7
页码：2164-2192
DOI：10.1214/13-EJS842
语种：English
出版社：Institute of Mathematical Statistics
摘要：In this paper, we propose corrections to the likelihood ratio test and John’s test for sphericity in large-dimensions. New formulas for the limiting parameters in the CLT for linear spectral statistics of sample covariance matrices with general fourth moments are first established. Using these formulas, we derive the asymptotic distribution of the two proposed test statistics under the null. These asymptotics are valid for general population, i.e. not necessarily Gaussian, provided a finite fourth-moment. Extensive Monte-Carlo experiments are conducted to assess the quality of these tests with a comparison to several existing methods from the literature. Moreover, we also obtain their asymptotic power functions under the alternative of a spiked population model as a specific alternative.
关键词：Large-dimensional data;large-dimensional sam ple covariance matrix;sphericity;likelihood ratio test;John’s test;Nagao’s test;CLT for linear spectral statistics;spiked population model.