We investigate conditions under which estimators of the form X + aU'Ug(X) dominate X when X, a p - 1 vector, and U, an m - 1 vector, are distributed such that [X1, X2,..., Xp, U1, U2,..., Up]'/[sigma] has a spherically symmetric distribution about [[theta]1, [theta]2,..., [theta]p, 0, 0,...,...

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...

For X one observation on a p-dimensional (p = 4) spherically symmetric (s.s.) distribution about [theta], minimax estimators whose risks dominate the risk of X (the best invariant procedure) are found with respect to general quadratic loss, L([delta], [theta]) = ([delta] - [theta])' D([delta] -...

For p 4 and one observation X on a p-dimensional spherically symmetric distribution, minimax estimators of Theta whose risks are smaller than the risk of X (the best invariant estimator) are found when the loss is a nondecreasing concave function of quadratic loss. For n observations X1, X2, ......

This paper presents an expository development of Stein estimation with substantial emphasis of exact results for spherically symmetric distributions. The themes of the paper are: a) that the improvement possible over the best invariant estimator via shrinkage estimation is not surprising but...

This paper presents an expository development of Bayesian estimation with substantial emphasis on exact results for the multivariate normal location models with respect to squared error loss. From the time Stein, in 1956, showed the inadmissibility of the best invariant estimator when sampling...

Families of minimax estimators are found for the location parameter of a p-variate (pgt; or = 3) spherically symmetric unimodal(s.s.u.)distribution with respect to general quadratic loss. The estimators of James and Stein, Baranchik, Bock and Strawderman are all considered for this general...

This paper reviews advances in Stein-type shrinkage estimation for spherically symmetric distributions. Some emphasis is placed on developing intuition as to why shrinkage should work in location problems whether the underlying population is normal or not. Considerable attention is devoted to...