Generalized Bayes minimax estimators of location vectors for spherically symmetric distributions with residual vector

We consider estimation of the mean vector, $\theta $ , of a spherically symmetric distribution with known scale parameter under quadratic loss and when a residual vector is available. We show minimaxity of generalized Bayes estimators corresponding to superharmonic priors with a non decreasing Laplacian of the form $\pi (\Vert \theta \Vert ^{2})$ , under certain conditions on the generating function $f(\cdot )$ of the sampling distributions. The class of sampling distributions includes certain variance mixtures of normals.