关键词: 非齐次线性估计, 线性估计类, 一切估计组成的估计类, 二次矩阵损失函数

Abstract:

This paper studies the admissibility of matrix nonhomogeneous linear estimators of an estimable parameter matrix linear function in multivariate linear models 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 without normality assumption. Under normality assumption, a sufficient condition that a matrix nonhomogeneous linear estimator is admissible in the class of all matrix estimators is derived.

Key words: Admissibility, Multivariate linear models, Nonhomogeneous linear estimators, Class of all linear estimators, Class of all matrix estimators, Quadratic matrix loss functions