Bayes minimax estimation of the multivariate normal mean vector for the case of common unknown variance

We investigate the problem of estimating the mean vector [theta] of a multivariate normal distribution with covariance matrix [sigma]2Ip, when [sigma]2 is unknown, and where the loss function is . We find a large class of (proper and generalized) Bayes minimax estimators of [theta], and show that the result of Strawderman (1973) [8] is a special case of our result. Since a large subclass of the estimators found are proper Bayes, and therefore admissible, the class of admissible minimax estimators is substantially enlarged as well.