In estimating a multivariate normal mean vector Sengupta and Sen (1991) have shown that Stein-type shrinkage estimator improves upon MLE when the shrinkage is made in a positively homogeneous subset. In this paper it is shown that Stein-type shrinkage estimator gives improvement for a wide class of restricted subsets by simply using an integration by parts after applying the transformation to polar coordinates. Further, it is generalized to the case where the shrinkage factor depends on not only the norm but also the direction of the observed vector. Some applications to the estimators shrinking towards a ball and a hyperplane are given.
