Improving on Minimum Risk Equivariant and Linear Minimax Estimators of Bounded Multivariate Location Parameters

Abstract

We propose improvements under squared error loss of the minimum risk equivariant and the linear minimax estimators for estimating the location parameter θ of a p-variate spherically symmetric distribution, with θ restricted to a ball of radius m centered at the origin. Our construction of explicit improvements relies on a multivariate version of Kubokawa’s Integral Expression of Risk Difference (IERD) method. Applications are given for univariate distributions, for the multivariate normal, and for scale mixture of multivariate normal distributions.