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Hypothesis testing for the identity of high-dimensional covariance matrices

Author

Listed:
  • Qian, Manling
  • Tao, Li
  • Li, Erqian
  • Tian, Maozai

Abstract

A new test statistic is proposed by utilizing the eigenvalues of the sample covariance matrix for the identity test. Under some general assumptions, asymptotic distributions of the proposed test statistic T and tests proposed in previous literature (denoted as Ts,T1,T2) are given. Simulations are also conducted to evaluate their performance in a finite sample.

Suggested Citation

  • Qian, Manling & Tao, Li & Li, Erqian & Tian, Maozai, 2020. "Hypothesis testing for the identity of high-dimensional covariance matrices," Statistics & Probability Letters, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:stapro:v:161:y:2020:i:c:s016771522030002x
    DOI: 10.1016/j.spl.2020.108699
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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. 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.
    3. 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.
    4. 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.
    5. Li, Weiming & Qin, Yingli, 2014. "Hypothesis testing for high-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 108-119.
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    Cited by:

    1. Deepak Nag Ayyala & Santu Ghosh & Daniel F. Linder, 2022. "Covariance matrix testing in high dimension using random projections," Computational Statistics, Springer, vol. 37(3), pages 1111-1141, July.

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