| 多元线性模型中回归系数的线性可容许估计 |
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| 引用本文： | 曹明响,孔繁超.多元线性模型中回归系数的线性可容许估计[J].应用数学学报,2009,32(5). |
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| 作者姓名： | 曹明响 孔繁超 |
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| 作者单位： | 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 |
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| 基金项目： | 安徽省高等学校优秀青年人才 |
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| 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.
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| 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 |
Admissibility for Linear Estimators to Regression Coefficients in a Multivariate Linear Models |
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| CAO MINGXIANG,KONG FANCHAO.Admissibility for Linear Estimators to Regression Coefficients in a Multivariate Linear Models[J].Acta Mathematicae Applicatae Sinica,2009,32(5). |
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| Authors: | CAO MINGXIANG KONG FANCHAO |
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| Abstract: | 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. |
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| Keywords: | multivariate linear model matrix balanced loss function linear estimators admissibility |
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