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April, 1995 Estimation of a Loss Function for Spherically Symmetric Distributions in the General Linear Model
Dominique Fourdrinier, Martin T. Wells
Ann. Statist. 23(2): 571-592 (April, 1995). DOI: 10.1214/aos/1176324536

Abstract

This paper is concerned with estimating the loss of a point estimator when sampling from a spherically symmetric distribution. We examine the canonical setting of a general linear model where the dimension of the parameter space is greater than 4 and less than the dimension of the sampling space. We consider two location estimators--the least squares estimator and a shrinkage estimator--and we compare their unbiased loss estimator with an improved loss estimator. The domination results are valid for a large class of spherically symmetric distributions and, in so far as the sampling distribution does not need to be precisely specified, the estimates have desirable robustness properties.

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Dominique Fourdrinier. Martin T. Wells. "Estimation of a Loss Function for Spherically Symmetric Distributions in the General Linear Model." Ann. Statist. 23 (2) 571 - 592, April, 1995. https://doi.org/10.1214/aos/1176324536

Information

Published: April, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0829.62011
MathSciNet: MR1332582
Digital Object Identifier: 10.1214/aos/1176324536

Subjects:
Primary: 62A99
Secondary: 62C05, 62C15, 62C99, 62F35

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.23 • No. 2 • April, 1995
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