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A robust test for sphericity of high-dimensional covariance matrices

Author

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  • Tian, Xintao
  • Lu, Yuting
  • Li, Weiming

Abstract

This paper discusses the problem of testing the sphericity of a covariance matrix in high-dimensional frameworks. A new test procedure is put forward by taking the maximum of two existing statistics which are proved weakly independent in our settings. Asymptotic distribution of the new statistic is derived for generally distributed population with a finite fourth moment. Extensive simulations demonstrate that the proposed test has a great improvement in robustness of power against various models under the alternative hypothesis.

Suggested Citation

  • Tian, Xintao & Lu, Yuting & Li, Weiming, 2015. "A robust test for sphericity of high-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 217-227.
    • Handle: RePEc:eee:jmvana:v:141:y:2015:i:c:p:217-227
    DOI: 10.1016/j.jmva.2015.07.010
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    References listed on IDEAS

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    1. Srivastava, Muni S. & Kollo, Tõnu & von Rosen, Dietrich, 2011. "Some tests for the covariance matrix with fewer observations than the dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1090-1103, July.
    2. Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
    3. Chen, Song Xi & Zhang, Li-Xin & Zhong, Ping-Shou, 2010. "Tests for High-Dimensional Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 810-819.
    4. Fisher, Thomas J. & Sun, Xiaoqian & Gallagher, Colin M., 2010. "A new test for sphericity of the covariance matrix for high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2554-2570, November.
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    Cited by:

    1. Wang, Zhendong & Xu, Xingzhong, 2021. "Testing high dimensional covariance matrices via posterior Bayes factor," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    2. Chen, Jiaqi & Zhang, Yangchun & Li, Weiming & Tian, Boping, 2018. "A supplement on CLT for LSS under a large dimensional generalized spiked covariance model," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 57-65.
    3. Zhendong Wang & Xingzhong Xu, 2021. "High-dimensional sphericity test by extended likelihood ratio," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1169-1212, November.

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