Estimation of location parameters for spherically symmetric distributions

Jian-Lun Xu and Grant Izmirlian

Journal of Multivariate Analysis, 2006, vol. 97, issue 2, 514-525

Abstract: Estimation of the location parameters of a px1 random vector with a spherically symmetric distribution is considered under quadratic loss. The conditions of Brandwein and Strawderman [Ann. Statist. 19(1991) 1639-1650] under which estimators of the form dominate are (i) where -h is superharmonic, (ii) is nonincreasing in R, where has a uniform distribution in the sphere centered at with a radius R, and (iii) . In this paper, we not only drop their condition (ii) to show the dominance of over but also obtain a new bound for a which is sometimes better than that obtained by Brandwein and Strawderman. Specifically, the new bound of a is 0

Keywords: James-Stein; type; estimators; Location; parameters; Spherical; distributions; Quadratic; loss; Risk; function (search for similar items in EconPapers)
Date: 2006
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