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Local expectations of the population spectral distribution of a high-dimensional covariance matrix

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  • Weiming Li

Abstract

This paper discusses the relationship between the population spectral distribution and the limit of the empirical spectral distribution in high-dimensional situations. When the support of the limiting spectral distribution is split into several intervals, the population one gains a meaningful division, and general functional expectations of each part from the division, referred as local expectations, can be formulated as contour integrals around these intervals. Basing on these knowledge we present consistent estimators of the local expectations and prove a central limit theorem for them. The results are then used to analyze an estimator of the population spectral distribution in recent literature. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Weiming Li, 2014. "Local expectations of the population spectral distribution of a high-dimensional covariance matrix," Statistical Papers, Springer, vol. 55(2), pages 563-573, May.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:2:p:563-573
    DOI: 10.1007/s00362-013-0501-6
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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. 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.
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    Cited by:

    1. Tingting Zou & Shurong Zheng & Zhidong Bai & Jianfeng Yao & Hongtu Zhu, 2022. "CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data," Statistical Papers, Springer, vol. 63(2), pages 605-664, April.
    2. Ningning Xia & Zhidong Bai, 2019. "Convergence rate of eigenvector empirical spectral distribution of large Wigner matrices," Statistical Papers, Springer, vol. 60(3), pages 983-1015, June.

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