Loss Estimation for Spherically Symmetrical Distributions

D. Fourdrinier and M. T. Wells

Journal of Multivariate Analysis, 1995, vol. 53, issue 2, 311-331

Abstract: In this paper we consider the problem of estimating the quadratic loss of point estimators of a location parameter for a family of spherically symmetric distributions. We compare the unbiased loss estimator of the minimax estimator with a new shrinkage type loss estimator. Conditions on the distributions for the domination of competing estimators are given. It is shown that, in addition to the class of scale mixtures of normal distributions, there exists a more general family for which the domination results hold.

Date: 1995
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