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Estimating a covariance matrix of a normal distribution with unknown mean. (English) Zbl 0826.62041
Summary: For the covariance matrix of the multivariate normal distribution with an unknown mean vector, discontinuous or continuous Stein type truncated estimators have been proposed. This article summarizes a series of recent results and obtains an improved and generalized Bayes estimator based on the Brown-Brewster-Zidek method [L. D. Brown, Ann. Math. Stat. 39, 29-48 (1968; Zbl 0162.499); J. F. Brewster and J. V. Zidek, Ann. Stat. 2, 21-38 (1974; Zbl 0275.62006)] well known in the univariate case. The asymptotic risk expansions of the estimators are derived, numerically investigated, and it is revealed that the risk-reductions of the generalized Bayes estimator and an empirical Bayes estimator are considerably great in the large dimensional case.

62H12 Estimation in multivariate analysis
62C12 Empirical decision procedures; empirical Bayes procedures
62F15 Bayesian inference