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Empirical Bayes estimation of the covariance matrix of a normal distribution with unknown mean under an entropy loss. (English) Zbl 0770.62005
Summary: In the estimation of the covariance matrix of the multivariate normal distribution with unknown mean vector, B. K. Sinha and M. Ghosh [Stat. Decis. 5, 201-227 (1987; Zbl 0634.62050)] proposed a truncated estimator improving on the best invariant one relative to the entropy loss. The purpose of the paper is to derive an empirical Bayes estimator based on conjugate priors and to prove that it is better than the Sinha-Ghosh estimator. An empirical Bayes estimator for the generalized variance is also given and it is shown to be identical to the usual Stein type truncated estimator.

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