We consider the problem of estimating a p-dimensional parameter [theta]=([theta]1,...,[theta]p) when the observation is a p+k vector (X,U) where dim X=p and where U is a residual vector with dim U=k. The distributional assumption is that (X,U) has a spherically symmetric distribution around...

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...

For independently distributed observables: Xi~N([theta]i,[sigma]2),i=1,...,p, we consider estimating the vector [theta]=([theta]1,...,[theta]p)' with loss ||d-[theta]||2 under the constraint , with known [tau]1,...,[tau]p,[sigma]2,m. In comparing the risk performance of Bayesian estimators...

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...

The theory of Bayesian least squares is developed for a general and more tangible notion of conjugacy than in models which make the more conventional assumption of normality. This paper is primarily concerned with extending the results of classical conjugate normal-normal Bayesian analysis to...

Let X~f([short parallel]x-[theta][short parallel]2) and let [delta][pi](X) be the generalized Bayes estimator of [theta] with respect to a spherically symmetric prior, [pi]([short parallel][theta][short parallel]2), for loss [short parallel][delta]-[theta][short parallel]2. We show that if...

The estimation of the location parameter of a spherically symmetric distribution was greatly improved by Berger and Brandwein. But the authors conditions on the shrinkage estimators depend upon the complete knowledge, up to the location parameter, of the distribution of the observations. We give...

Bayes estimation of the mean of a variance mixture of multivariate normal distributions is considered under sum of squared errors loss. We find broad class of priors (also in the variance mixture of normal class) which result in proper and generalized Bayes minimax estimators. This paper extends...

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...

The estimation of the location parameter of an l1-symmetric distribution is considered. Specifically when a p-dimensional random vector has a distribution that is a mixture of uniform distributions on the l1-sphere, we investigate a general class of estimators of the form [delta]=X+g. Under the...