# On the best equivariant estimator of mean of a multivariate normal population

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## Abstract

Let X1,...,Xn (n>1, p>1) be independently and identically distributed normal p-vectors with mean [mu] and covariance matrix ([mu]'[mu]/C2)I, where the coefficient of variation C is known. The authors have obtained the best equivariant estimator of [mu] under the loss function L([mu]d)=([mu]-d)'([mu]-d/[mu]'[mu]) They have compared the best equivariant estimator with 3 other wellknown equivariant estimators of [mu] and have shown that the best equivariant estimator is markedly superior to others when C-->0.

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