矩阵损失函数下回归系数矩阵的非齐次线性估计的可容许性

ADMISSIBLE MATRIX NONHOMOGENEOUS LINEAR ESTIMATES UNDER A QUADRATIC MATRIX LOSS FUNCTION

在二次矩阵损失函数下研究了协方差矩阵未知的多元线性模型中回归系数矩阵的可估线性函数的矩阵非齐次线性估计的可容许性,给出了矩阵非齐次线性估计在线性估计类中可容许的一个充要条件.

This paper studies admissibility of matrix nonhomogeneous linear estimators for an estimable linear function of the parameter matrix in a multivariate linear model with completely unknown covariance matrix under a quadratic matrix loss function.A necessary and sufficient condition is given for a matrix nonhomogeneous linear estimator to be admissible in the class of all matrix linear estimators.