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Improved estimation of a covariance matrix in an elliptically contoured matrix distribution

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  • Leung, Pui Lam
  • Ng, Foon Yip

Abstract

In this paper, the problem of estimating the covariance matrix of the elliptically contoured distribution (ECD) is considered. A new class of estimators which shrink the eigenvalues towards their arithmetic mean is proposed. It is shown that this new estimator dominates the unbiased estimator under the squared error loss function. Two special classes of ECD, namely, the multivariate-elliptical t distribution and the [var epsilon]-contaminated normal distribution are considered. A simulation study is carried out and indicates that this new shrinkage estimator provides a substantial improvement in risk under most situations.

Suggested Citation

  • Leung, Pui Lam & Ng, Foon Yip, 2004. "Improved estimation of a covariance matrix in an elliptically contoured matrix distribution," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 131-137, January.
    • Handle: RePEc:eee:jmvana:v:88:y:2004:i:1:p:131-137
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    References listed on IDEAS

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    1. Haff, L. R., 1979. "An identity for the Wishart distribution with applications," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 531-544, December.
    2. Pui Leung & Wai Chan, 1998. "Estimation of the Scale Matrix and its Eigenvalues in the Wishart and the Multivariate F Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(3), pages 523-530, September.
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    Cited by:

    1. Besson, Olivier & Abramovich, Yuri I., 2014. "Invariance properties of the likelihood ratio for covariance matrix estimation in some complex elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 237-246.
    2. Ye, Ren-Dao & Wang, Song-Gui, 2009. "Improved estimation of the covariance matrix under Stein's loss," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 715-721, March.
    3. Fourdrinier, Dominique & Mezoued, Fatiha & Wells, Martin T., 2016. "Estimation of the inverse scatter matrix of an elliptically symmetric distribution," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 32-55.

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