### K. KRISHNAMOORTHY

Department of Statistics, Temple University, Philadelphia, PA 19122, U.S.A.

(Received December 4, 1989; revised June 6, 1990)

Abstract.    Let X1,...., XN be independent observations from Np(mu, Sigma1) and Y1,...., YN be independent observations from Np(mu, Sigma2). Assume that Xi's and Yi's are independent. An unbiased estimator of mu which dominates the sample mean \bar X for p > 1 under the loss function L(mu, ^mu) = (^mu - mu)'Sigma1-1(^mu-mu) is suggested. The exact risk (under L) of the new estimator is also evaluated.

Key words and phrases:    Common mean vector, unbiased estimator, Wishart and noncentral Wishart distributions.

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