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Equivariant estimators of the covariance matrix. (English) Zbl 0702.62048
Summary: Given a Wishart matrix S \([S\sim W_ p(n,\Sigma)]\) and an independent multinormal vector X \([X\sim N_ p(\mu,\Sigma)]\), equivariant estimators of \(\Sigma\) are proposed. These estimators dominate the best multiple of S and the Stein-type truncated estimators.

MSC:
62H12 Estimation in multivariate analysis
62A01 Foundations and philosophical topics in statistics
62C15 Admissibility in statistical decision theory
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[1] Brewster, Improving on equivariant estimators, Ann. Statist. 2 pp 21– (1974) · Zbl 0275.62006
[2] Dey, Estimation of covariance matrix under Stein’s loss, Ann. Statist. 13 pp 1581– (1985)
[3] Haff, Empirical Bayes estimation of the multivariate normal covariance matrix, Ann. Statist. 8 pp 586– (1980) · Zbl 0441.62045
[4] James, Estimation with quadratic loss, Proc. Fourth Berkeley Symp. Statist. Probab. 1 pp 361– (1961) · Zbl 1281.62026
[5] Kubokawa, Improved estimation of a covariance matrix under quadratic loss, Statist. Probab. Lett. 8 pp 69– (1989) · Zbl 0667.62040
[6] Olkin, Statistical Decision Theory and Related Topics pp 2– (1977)
[7] Sinha, Inadmissibility of the best equivariant estimator of the variance-covariance matrix and the generalized variance under entropy loss, Statist. Decisions 5 pp 201– (1987) · Zbl 0634.62050
[8] Stein, Inadmissibility of the usual estimator of the variance of a normal distribution with unknown mean, Ann. Inst. Statist. Math. 16 pp 155– (1964) · Zbl 0144.41405
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