摘要
假设一个n维随机向量Y服从正态分布N(β,σ2In)。在二次损失下,当n≥3和σ2已知时,Stein在1956年指出Y不是β的容许估计,这是统计判决理论中一个著名的结果.成平在1982年对Stein结果给出了一个有趣的补充,他证明了当σ2未知时,Y是β的容许估计.这篇文章是成平结果的一般化,即在一个宽广的分布类中,证明了当方差未知时,回归系数最小二乘估计是容许的.这表明当方差未知时,回归系数最小二乘估计是一个适合的估计.
Suppose an ndimension random vector Y is distributed to the normal distribution N(β,σ2In). When σ2 is known and n≥3, Stein pointed out that Y is an inadmissible estimator of β under the quadratic loss. This is a well known result in statistical decision theory. Cheng gave an interesting supplement of Stein's result. He proved that Y is admissible when σ2 is unknown. This paper is a generalization of the result in . We prove that the least squares estimator of the regression coeffcient is admissible for a wide class of distributions when the variance σ2 is unknown. This shows that the usual estimator of the regression coeffcient is available when σ2 is unknown.
出处
《华中师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2003年第3期286-289,共4页
Journal of Central China Normal University：Natural Sciences
基金
The research was supported by the Natural Science Foundation of China(1 9941 0 0 3 ).
关键词
二次损失
最小二乘估计
容许性
admissibility
least squares estimator
quadratic loss
