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

Admissibility of Linear Estimator in Growth Curve Model with Respect to a Incomplete Ellipsoidal Restriction Under the Matrix Loss

对于带有不完全椭球约束的生长曲线模型Y=XBZ+ε,ε^(0,σ2VI),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.

For the growth curve model with respect to a incomplete ellipsoidal restriction Y=XBZ＋ε,ε^（0,σ2VI）,X（B-B0）Z′NZ（B-B0）′X′≤σ^2In, This paper gives the necessary and sufficient conditions of KBL in the class of homogeneous linear estimators JH and nonhomogeneous linear estimators H. 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.