SHRINKAGE DOMINATION IN A MULTIVARIATE COMMON-MEAN PROBLEM

Consider the problem of estimating the p X 1 mean vector theta-under expected squared error loss, based on the observation of two independent multivariate normal vectors Y1 approximately N(p)(theta, sigma-2I) and Y2 approximately N(p)(theta, lambda-sigma-2I) when lambda-and sigma-2 are unknown. For p greater-than-or-equal-to 3, estimators of the form delta-eta = eta-Y1 + (1 - eta)Y2 where-eta is a fixed number in (0,1), are shown to be uniformly dominated in risk by Stein estimators in spite of the fact that independent estimates of scale are unavailable. A consequence of this result is that when lambda-is assumed known, shrinkage domination is robust to incorrect specification of lambda.