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On generalized expectation-based estimation of a population spectral distribution from high-dimensional data

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  • Weiming Li
  • Jianfeng Yao

Abstract

This paper discusses the problem of estimating the population spectral distribution from high-dimensional data. We present a general estimation procedure that covers situations where the moments of this distribution fail to identify the model parameters. The main idea is to use generalized functional expectations as a substitute for the moments. Beyond the consistency, we also prove a central limit theorem for the proposed estimator. Simulation experiments illustrate the implementation of the estimation procedure. An application to the analysis of the eigenvalues of the sample correlation matrix of S&P 500 daily stock returns is proposed. Copyright The Institute of Statistical Mathematics, Tokyo 2015

Suggested Citation

  • Weiming Li & Jianfeng Yao, 2015. "On generalized expectation-based estimation of a population spectral distribution from high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 359-373, April.
    • Handle: RePEc:spr:aistmt:v:67:y:2015:i:2:p:359-373
    DOI: 10.1007/s10463-014-0452-2
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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. Baik, Jinho & Silverstein, Jack W., 2006. "Eigenvalues of large sample covariance matrices of spiked population models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1382-1408, July.
    3. 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. Qin, Yingli & Li, Weiming, 2016. "Testing the order of a population spectral distribution for high-dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 75-82.
    2. Wen, Jun, 2018. "Estimation of two high-dimensional covariance matrices and the spectrum of their ratio," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 1-29.

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