ESTIMATION OF A MULTIVARIATE NORMAL-MEAN VECTOR AND LOCAL IMPROVEMENTS

Let X be a (p x 1) random vector following a multivariate normal distr ibution with mean vector theta and a known dispersion matrix. Also sup pose we have an extra observation U, independent of X, whose distribut ion is completely known. In this article we first develop estimators o f theta, combining both X and U, which are similar to the James-Stein estimator but can give substantial risk improvement over it when theta is assumed to be in a neighborhood of a known value. Estimators based only on X are then developed which can give further improvements.