The Annals of Statistics

Estimation of a Loss Function for Spherically Symmetric Distributions in the General Linear Model

Dominique Fourdrinier and Martin T. Wells

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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.

Article information

Source
Ann. Statist., Volume 23, Number 2 (1995), 571-592.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176324536

Digital Object Identifier
doi:10.1214/aos/1176324536

Mathematical Reviews number (MathSciNet)
MR1332582

Zentralblatt MATH identifier
0829.62011

JSTOR
links.jstor.org

Subjects
Primary: 62A99: None of the above, but in this section
Secondary: 62C05: General considerations 62C15: Admissibility 62C99: None of the above, but in this section 62F35: Robustness and adaptive procedures

Keywords
Spherical symmetry loss estimation shrinkage estimation conditional inference

Citation

Fourdrinier, Dominique; Wells, Martin T. Estimation of a Loss Function for Spherically Symmetric Distributions in the General Linear Model. Ann. Statist. 23 (1995), no. 2, 571--592. doi:10.1214/aos/1176324536. https://projecteuclid.org/euclid.aos/1176324536


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