| 带有不完全椭球约束的生长曲线模型中线性估计的可容许性 |
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| 引用本文： | 方龙祥,郭大伟.带有不完全椭球约束的生长曲线模型中线性估计的可容许性[J].大学数学,2008,24(4). |
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| 作者姓名： | 方龙祥 郭大伟 |
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| 作者单位： | 安徽师范大学,数学计算机科学学院,安徽,芜湖,241000 |
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| 基金项目： | 安徽省教育厅科研项目，安徽师范大学校科研和教改项目 |
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| 摘 要： | 对于带有不完全椭球约束的生长曲线模型Y=XBZ+ε,ε~(0,σ2VI),X(B-B0)Z′NZ(B-B0)′X′≤σ2In,本文在矩阵损失函数(d-KBL)(d-KBL)′下给出了KBL在类齐次线性估计类LH与非齐次线性估计类LI中可容许的充要条件.本文的结果表明线性估计在非齐次线性估计类中的可容许性与椭球的中心B0无关,而齐次线性估计在齐次线性估计类中的可容许性与B0有关.
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| 关 键 词： | 不完全椭球约束 可容许性 生长曲线模型 |
Admissibility of Linear Estimator in Growth Curve Model with Respect to a Incomplete Ellipsoidal Restriction Under the Matrix Loss |
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| FANG Long-xiang,GUO Da-wei.Admissibility of Linear Estimator in Growth Curve Model with Respect to a Incomplete Ellipsoidal Restriction Under the Matrix Loss[J].College Mathematics,2008,24(4). |
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| Authors: | FANG Long-xiang GUO Da-wei |
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| Abstract: | For the growth curve model with respect to a incomplete ellipsoidal restrictionY=XBZ+ε,～(0,σ2VI),X(B-B0)Z′NZ(B-B0)′X′≤σ2In.This paper gives the necessary and sufficient conditions of KBL in the class of homogeneous linear estimators LH and non-homogeneous linear estimators LI,under the matrix loss function(d-KBL)(d-KBL)′.The results shown that the admissibility of linear estimator in the class of non-homogeneous linear estimators is independent on B0,but the admissibility of homogeneous linear estimator in the class of homogeneous linear estimators is dependent on B0. |
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| Keywords: | incomplete ellipsoidal restriction admissibility growth curve model |
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