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A Stein’s approach to covariance matrix estimation using regularization of Cholesky factor and log-Cholesky metric

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  • Besson, Olivier
  • Vincent, François
  • Gendre, Xavier

Abstract

We consider a Stein’s approach to estimate a covariance matrix using regularization of the sample covariance matrix Cholesky factor. We propose a method to estimate accurately the regularization vector which minimizes the risk associated with the recently introduced log-Cholesky metric.

Suggested Citation

  • Besson, Olivier & Vincent, François & Gendre, Xavier, 2020. "A Stein’s approach to covariance matrix estimation using regularization of Cholesky factor and log-Cholesky metric," Statistics & Probability Letters, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:stapro:v:167:y:2020:i:c:s0167715220301966
    DOI: 10.1016/j.spl.2020.108893
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2016. "Unified improvements in estimation of a normal covariance matrix in high and low dimensions," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 233-248.
    3. Sheena, Yo & Takemura, Akimichi, 1992. "Inadmissibility of non-order-preserving orthogonally invariant estimators of the covariance matrix in the case of Stein's loss," Journal of Multivariate Analysis, Elsevier, vol. 41(1), pages 117-131, April.
    4. Tsukuma, Hisayuki, 2016. "Estimation of a high-dimensional covariance matrix with the Stein loss," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 1-17.
    5. Ikeda, Yuki & Kubokawa, Tatsuya & Srivastava, Muni S., 2016. "Comparison of linear shrinkage estimators of a large covariance matrix in normal and non-normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 95-108.
    6. Haff, L. R., 1979. "An identity for the Wishart distribution with applications," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 531-544, December.
    7. Konno, Yoshihiko, 2009. "Shrinkage estimators for large covariance matrices in multivariate real and complex normal distributions under an invariant quadratic loss," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2237-2253, November.
    8. Arjun K. Gupta & Daya K. Nagar, 2000. "Matrix-variate beta distribution," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 24, pages 1-11, January.
    9. Perron, F., 1992. "Minimax estimators of a covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 43(1), pages 16-28, October.
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