Improved estimates of location in the presence of an unknown scale

Ann Cohen Brandwein and William E. Strawderman

Journal of Multivariate Analysis, 1991, vol. 39, issue 2, 305-314

Abstract: We investigate conditions under which estimators of the form X + aU'Ug(X) dominate X when X, a p - 1 vector, and U, an m - 1 vector, are distributed such that [X1, X2,..., Xp, U1, U2,..., Up]'/[sigma] has a spherically symmetric distribution about [[theta]1, [theta]2,..., [theta]p, 0, 0,..., 0]', where [sigma] is an unknown scale. Brandwein and Strawderman [2] have results for quadratic loss and we extend these results to concave functions of quadratic loss and to general quadratic loss.

Keywords: spherical; symmetry; quadratic; loss; concave; loss; James-Stein; estimation; location; parameter; unknown; scale; superharmonic; functions (search for similar items in EconPapers)
Date: 1991
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