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

Γ-minimax estimators are determined for the mean vector of a multivariate normaldistribution under arbitrary squared error loss.Thereby the set Γ consists of all priorswhose vector of first moments and matrix of second moments satisfy some given restric-tions.Necessary and sufficient conditions are derived which ensure a prior being leastfavourable in Γ and the unique Bayes estimator with respect to this prior being Γ-minimax.By applying these results the Γ-minimax estimator is explicitly found in some special casesor can be computed by solving a system of non-linear equations or by minimizing a quad-ratic form on a compact and convex set.

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.