Shrinkage Estimators under Spherical Symmetry for the General Linear Model

✍ Scribed by D. Cellier; D. Fourdrinier

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 457 KB
• Volume: 52
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1995.1018

✦ Synopsis

This paper is primarily concerned with extending the results of Brandwein and Strawderman in the usual canonical setting of a general linear model when sampling from a spherically symmetric distribution. When the location parameter belongs to a proper linear subspace of the sampling space, we give an unbiased estimator of the difference of the risks between the least squares estimator (\varphi_{0}) and a general shrinkage estimator (\varphi=\varphi_{0}-\left|X-\varphi_{0}\right|^{2} \cdot g=\varphi_{10}). We obtain a general condition of domination for (\varphi) over (\varphi_{0}) which is weaker than that of Brandwein and Strawderman. We do not need any superharmonicity condition on (g). Our results are valid for general quadratic loss. ' 1995 Academic Press. Inc.