On the construction of Bayes minimax estimators

Bayes estimation of the mean of a multivariate normal distribution is consi dered under quadratic loss. We show that, when particular spherical priors are used, the superharmonicity of the square root of the marginal density p rovides a viable method for constructing (possibly proper) Bayes (and admis sible) minimax estimators. Examples illustrate the theory; most notably it is shown that a multivariate Student-t prior yields a proper Bayes minimax estimate.