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Estimators of the location parameter under certain spherically symmetric distribution with stochastic analysis

Hobbad Lahoucine, Ouassou Idir

Abstract



In this article, we consider estimation of a location vector for a sub-classe of distributions that includes the spherically symmetric ones, in the presence of a known or unknown scale parameter. Specifically, for these distributions we obtain slightly more general conditions and larger classes of estimators than Steven N. Evans1 and Philip B. Stark (1996) under which estimators of the form X + g(X) dominate X for quadratic loss, using elementary
stochastic analysis to obtain a generalization of an integration by parts lemma due to Stein in the Gaussian case.

Keywords


spherical symmetry, quadratic loss, James-Stein estimation, stochastic analysis, Brownian motion.

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