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Estimation of scale matrix of elliptically contoured matrix distributions

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  • Li, Run-Ze
  • Fang, Kai-Tai

Abstract

In this paper, the problem of estimation of scale matrix is considered under entropy loss, quadratic loss and squared error loss. With respect to entropy and quadratic loss, we obtain the best estimator of [Sigma] having the form [alpha]Sx as well as having the form Tx[Delta]Tx', where Sx, Tx and [Delta] are given in the text, and obtain the minimax estimator of [Sigma] and the best equivariant estimator of [Sigma] with respect to the triangular transformations group. With respect to the squared error loss, we generalize the result of Dey and Srinivasan (1992).

Suggested Citation

  • Li, Run-Ze & Fang, Kai-Tai, 1995. "Estimation of scale matrix of elliptically contoured matrix distributions," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 289-297, September.
    • Handle: RePEc:eee:stapro:v:24:y:1995:i:4:p:289-297
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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. Dipak Dey, 1988. "Simultaneous estimation of eigenvalues," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(1), pages 137-147, March.
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    Cited by:

    1. 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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