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CLT for linear spectral statistics of high-dimensional sample covariance matrices in elliptical distributions

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  • Zhang, Yangchun
  • Hu, Jiang
  • Li, Weiming

Abstract

In this paper, we establish a new central limit theorem for the linear spectral statistics of high-dimensional sample covariance matrices. The underlying population belongs to the family of elliptical distributions, and the dimension of the population is allowed to grow to infinity, in proportion to the sample size. As an application, we construct confidence intervals for the model parameters of a Gaussian scale mixture.

Suggested Citation

  • Zhang, Yangchun & Hu, Jiang & Li, Weiming, 2022. "CLT for linear spectral statistics of high-dimensional sample covariance matrices in elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:jmvana:v:191:y:2022:i:c:s0047259x22000379
    DOI: 10.1016/j.jmva.2022.105007
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    References listed on IDEAS

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    1. 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.
    2. Changliang Zou & Liuhua Peng & Long Feng & Zhaojun Wang, 2014. "Multivariate sign-based high-dimensional tests for sphericity," Biometrika, Biometrika Trust, vol. 101(1), pages 229-236.
    3. Schott, James R., 2007. "A test for the equality of covariance matrices when the dimension is large relative to the sample sizes," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6535-6542, August.
    4. Silverstein, J. W. & Bai, Z. D., 1995. "On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 175-192, August.
    5. Weiming Li & Jianfeng Yao, 2018. "On structure testing for component covariance matrices of a high dimensional mixture," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(2), pages 293-318, March.
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    Cited by:

    1. Zhang, Yangchun & Zhou, Yirui & Liu, Xiaowei, 2023. "Applications on linear spectral statistics of high-dimensional sample covariance matrix with divergent spectrum," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).

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