Journal of the Korean Statistical Society
- 제15권2호
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- Pages.97-106
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- 1986
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- 1226-3192(pISSN)
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- 2005-2863(eISSN)
An Empiricla Bayes Estimation of Multivariate nNormal Mean Vector
초록
Assume that $X_1, X_2, \cdots, X_N$ are iid p-dimensional normal random vectors ($p \geq 3$) with unknown covariance matrix. The problem of estimating multivariate normal mean vector in an empirical Bayes situation is considered. Empirical Bayes estimators, obtained by Bayes treatmetn of the covariance matrix, are presented. It is shown that the estimators are minimax, each of which domainates teh maximum likelihood estimator (MLE), when the loss is nonsingular quadratic loss. We also derive approximate credibility region for the mean vector that takes advantage of the fact that the MLE is not the best estimator.
키워드