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

摘要

We consider estimation of the mean vector, θ, 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 π(||θ||~2), under certain conditions on the generating function f (·) of the sampling distributions. The class of sampling distributions includes certain variance mixtures of normals.