ESTIMATION OF A COMMON MULTIVARIATE NORMAL-MEAN VECTOR

Let X1,...,X(N) be independent observations from N(p)(mu,SIGMA-1) and Y1,...,Y(N) be independent observations from N(p) (mu,SIGMA-2). Assume that X(i)'s and Y(i)'s are independent. An unbiased estimator of mu-which dominates the sample mean XBAR for p greater-than-or-equal-to 1 under the loss function L(mu,mu) = (mu - mu)'SIGMA(1)-1(mu - mu) is suggested. The exact risk (under L) of the new estimator is also evaluated.