A Family of Admissible Minimax Estimators of the Mean of a Multivariate Normal Distribution

Let the p-component vector X be normally distributed with mean ξ and covariance σ²I where I denotes the identity matrix and σ is known. For estimating ξ with quadratic loss, it is known that X is minimax but inadmissible for p 3. We obtain a family of estimators which dominate X and are admissible. These estimators are, therefore, both minimax and admissible.