方差分量模型中回归系数的线性估计的可容许性的若干结果

SOME RESULTS ON THE ADMISSIBILITY OF A LINEAR ESTIMATOR OF REGRESSION COEFFICIENTS IN THE VARIANCE COMPONENTS MODEL

摘要: 考虑方差分量模型EY=Xβ,VAB（Y）=\sum_i=1^m \theta_i V_i,其中n×p矩阵X和非负定矩阵V_i（i=1,2,…,m）都是已知的,β∈R^p,θ_i≥0或θ_i>0（i=1,2,…,m）均为参数.设Sβ是线性可估的。在本文中,我们分别获得了在二次损失和矩阵损失下,关于Sβ的线性估计在线性估计类中可容许的若干结果,并在正态假设下,我们也讨论了线性估计在一切估计类中的可容许性。

Abstract: Consider the variance components model EY=Xβ,VAB（Y）=\sum_i=1^m \theta_i V_i where n×p matrix X and V_i（i=1,2,…,m） are known, andβ∈R^p,θ_i≥0 or θ_i>0（i=1,2,…,m） are parameters. Let Sβ be linear estimable. In this paper, some results for a linear estimator of Sβ to be admissible among linear estimators under the quadratic loss function and matrix loss function are obtained respectively. Under normalitsy assumption, we also consider the admissibility of the linear estimator among all the estimators.