多元线性模型中回归系数的线性可容许估计  

Admissibility for Linear Estimators to Regression Coefficients in a Multivariate Linear Models

作　　者：曹明响[1] 孔繁超[2] 

机构地区：[1]合肥师范学院数学系,合肥230061 [2]安徽大学数学科学学院,合肥230039

出　　处：《应用数学学报》2009年第5期951-957,共7页Acta Mathematicae Applicatae Sinica

基　　金：安徽省高等学校优秀青年人才基金项目(2009SQRZ154)

摘　　要：基于Zellner的平衡损失的思想,本文提出了矩阵形式的平衡损失函数,并在该损失函数下讨论了多元回归系数线性估计的可容许性.给出了六种不同形式的可容许定义,证明了这六种容许性在齐次和非齐次线性估计类中是一致的,且得到了其共同的可容许估计的充要条件.In this paper the matrix balanced loss functions are proposed according to Zellner＇s thought of balanced loss. Admissible linear estimators for regression coefficients in a multivariate linear model are investigated under the matrix balanced loss function under six kinds of definitions for admissibility. The six kinds of admissibility are proved to be identical in a class of homogeneous and nonhomogeneous linear estimators, and the sufficient and necessary conditions that linear estimators are admissible are obtained.

关 键 词：多元线性模型 矩阵平衡损失函数 线性估计 可容许性 

分 类 号：O212.4[理学—概率论与数理统计]