摘要
本文提出线性约束模型下回归系数的 stein 估计和双k类 stein 型估计的概念,二者均为回归系数β的非线性约束有偏估计。在均方误差意义下,证明了:当所含参数满足一定条件时,对一切β和σ~2,它们一致地优于β的约束最小二乘估计(?)_L。最后,将结果推广到较一般的线性约束模型。
In this paper we propose the Stein estimate _(sL)(c)and the double k-class Stein-type estimate _(sL)(k_1,k_2)for coefficient of regression in linear constrained regression model.Both are nonlinear and biased constrained estimates for β,the coefficient of regres- sion.Under the criteria of mean square error,we obtain that _(sL)(c)and _(sL)(k_1,k_2)uniform- ly improve the constrained least squares estimate _L of when c and k_1,k_2satisfy some condi- tions for all β and o^2.Finally we extend the results to more gerenalized linear constrained re- gression model.
出处
《山西师范大学学报（自然科学版）》
1992年第2期1-7,共7页
Journal of Shanxi Normal University(Natural Science Edition)
基金
本课题获山西省自然科学基金资助.
关键词
约束
LS
估计
约束
STEIN
估计
约束双
k
类
STEIN
型估计
均方误差
Constrained least squares estimate
Constrained Stein estimate
Constrained double k-class Stein-type estimate
Mean square error
