IMPROVED ESTIMATION UNDER PITMAN’S MEASURE OF CLOSENESS

STAVROS KOUROUKLIS

Department of Mathematics, University of Patras, 261 10 Patras, Greece

(Received February 17, 1995; revised July 31, 1995)

Abstract. Stein-type and Brown-type estimators are constructed for general families of distributions which improve in the sense of Pitman closeness on the closest (in a class) estimator of a parameter. The results concern mainly scale parameters but a brief discussion on improved estimation of location parameters is also included. The loss is a general continuous and strictly bowl shaped function, and the improved estimators presented do not depend on it, i.e., uniform domination is established with respect to the loss. The normal and inverse Gaussian distributions are used as illustrative examples. This work unifies and extends previous relevant results available in the literature.

Key words and phrases: Pitman’s measure of closeness, closest estimator, Stein-type estimator, Brown-type estimator, equivariant estimator, loss function, testimator.