ESTIMATION OF A LOSS FUNCTION FOR SPHERICALLY SYMMETRICAL DISTRIBUTIONS IN THE GENERAL LINEAR-MODEL

• 成果类型: Article
• 署名作者: FOURDRINIER, D; WELLS, MT
• 署名单位: Cornell University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324536
• 发表日期: 1995
• 页码: 571-592
• 关键词: confidence

摘要

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.