Stein estimation for non-normal spherically symmetric location families in three dimensions

We consider estimation of a location vector in the presence of known or unknown scale parameter in three dimensions. The technique of proof is Stein's integration by parts and it is used to cover several cases (e.g., non-unimodal distributions) for which previous results were known only in the cases of four and higher dimensions. Additionally, we give a necessary and sufficient condition on the shrinkage constant for improvement on the usual estimator for the spherical uniform distribution.