GAMMA-MINIMAX ESTIMATORS FOR THE MEAN VECTOR OF A MULTIVARIATE NORMAL DISTRIBUTION
Citation：
Chen Lanxiang.GAMMA-MINIMAX ESTIMATORS FOR THE MEAN VECTOR OF A MULTIVARIATE NORMAL DISTRIBUTION[J].Chinese Annals of Mathematics B,1991,12(1):45~57
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Authors：
Chen Lanxiang;
Abstract：
$\Gamma$-minimax estimators are determined for the mean vector of a multivariate normal distribution under arbitrary squared error loss. Thereby the set $\Gamma$ consists of all priors whose vector of first moments and matrix of second moments satisfy. some given restrictions. Necessary and sufficient conditions are derived which ensure a prior being least favourable in $\Gamma$ and the unique Bayes estimator with respect to this prior being $\Gamma$-minimax.By applying these results the $\Gamma$-minimax estimator is explicitly found in some special cases or ean be computed by solving a System of non-linear equation or by minimizing a quadratio form on a compact and convex set.
