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2013 On the sphericity test with large-dimensional observations
Qinwen Wang, Jianfeng Yao
Electron. J. Statist. 7: 2164-2192 (2013). DOI: 10.1214/13-EJS842


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.


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Qinwen Wang. Jianfeng Yao. "On the sphericity test with large-dimensional observations." Electron. J. Statist. 7 2164 - 2192, 2013.


Published: 2013
First available in Project Euclid: 10 September 2013

zbMATH: 1293.62127
MathSciNet: MR3104916
Digital Object Identifier: 10.1214/13-EJS842

Primary: 62H15
Secondary: 62H10

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society


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