We study estimation of a location vector restricted to a convex cone when the dimension, p, is at least 3. We find estimators which improve on the "usual" estimator (the MLE in the normal case) in the general case of a spherically symmetric distribution with unknown scale. The improved...

Consider the problem of estimating the mean vector [theta] of a random variable X in , with a spherically symmetric density f(||x-[theta]||2), under loss ||[delta]-[theta]||2. We give an increasing sequence of bounds on the shrinkage constant of Stein-type estimators depending on properties of...

Let X,V1,...,Vn-1 be n random vectors in with joint density of the formwhere both [theta] and [Sigma] are unknown. We consider the problem of the estimation of [theta] with the invariant loss ([delta]-[theta])'[Sigma]-1([delta]-[theta]) and propose estimators which dominate the usual estimator...

When estimating, under quadratic loss, the location parameter[theta]of a spherically symmetric distribution with known scale parameter, we show that it may be that the common practice of utilizing the residual vector as an estimate of the variance is preferable to using the known value of the...

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...

In the GMANOVA model or equivalent growth curve model, shrinkage effects on the MLE (maximum likelihood estimator) are considered under an invariant risk matrix. We first study the fundamental structure of the problem through which we decompose the estimation problem into some conditional...

Zellner ((1994) in: Gupta, S.S., Berger, J.O. (Eds.), Statistical Decision Theory and Related Topics. Springer, New York, pp. 371-390), introduced the notion of a balanced loss function in the context of a general linear model to reflect both goodness of fit and precision of estimation. We study...