Admissible Bayes equivariant estimation of location vectors for spherically symmetric distributions with unknown scale

This paper investigates estimation of the mean vector under invariant quadratic loss for a spherically symmetric location family with a residual vector with density of the form f(x,u)=.(p+n)/2f(.{.x...2+.u.2}), where . is unknown. We show that the natural estimator x is admissible for p=1,2. Also, for p.3, we find classes of generalized Bayes estimators that are admissible within the class of equivariant estimators of the form {1..(x/.u.)}x. In the Gaussian case, a variant of the James.Stein estimator, [1.{(p.2)/(n+2)}/{.x.2/.u.2+(p.2)/(n+2)+1}]x, which dominates the natural estimator x, is also admissible within this class. We also study the related regression model.