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.
Publié le : 1995-04-14
Classification:
Spherical symmetry,
loss estimation,
shrinkage estimation,
conditional inference,
62A99,
62C05,
62C15,
62C99,
62F35
@article{1176324536,
author = {Fourdrinier, Dominique and Wells, Martin T.},
title = {Estimation of a Loss Function for Spherically Symmetric Distributions in the General Linear Model},
journal = {Ann. Statist.},
volume = {23},
number = {6},
year = {1995},
pages = { 571-592},
language = {en},
url = {http://dml.mathdoc.fr/item/1176324536}
}
Fourdrinier, Dominique; Wells, Martin T. Estimation of a Loss Function for Spherically Symmetric Distributions in the General Linear Model. Ann. Statist., Tome 23 (1995) no. 6, pp. 571-592. http://gdmltest.u-ga.fr/item/1176324536/