A UNIFIED APPROACH TO IMPROVING EQUIVARIANT ESTIMATORS

• 成果类型: Article
• 署名作者: KUBOKAWA, T
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325369
• 发表日期: 1994
• 页码: 290-299
• 关键词: bayes minimax estimators; confidence-intervals; normal variance

摘要

In the point and interval estimation of the variance of a normal distribution with an unknown mean, the best affine equivariant estimators are dominated by Stein's truncated and Brewster and Zidek's smooth procedures, which are separately derived. This paper gives a unified approach to this problem by using a simple definite integral and provides a class of improved procedures in both point and interval estimation of powers of the scale parameter of normal, lognormal, exponential and Pareto distributions. Finally, the same method is applied to the improvement on the James-Stein rule in the simultaneous estimation of a multinormal mean.