GAMMA-MINIMAX ESTIMATORS FOR THE MEAN VECTOR OF A MULTIVARIATE NORMAL DISTRIBUTION

$\Gamma$-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.