方差分量模型中回归系数的线性估计的可容许性
Admissibility of Linear Estimators of Regression Coefficient in a Variance Component Model
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摘要: 考虑方差分量模型\ep Y=X\beta,\;\cov(Y)=\tsm_i=1^m\theta_iV_i, 其中n\times p矩阵X和非负定矩阵V_i\;(i=1,2,\cdots,m)都是已知的, \beta\in R^p,\;\theta_i\geq 0或\theta_i>0\;(i=1,2,\cdots,m)均为参数\bd 在本文中, 我们在二次损失下, 当\mu(X) \subset\mu(V)时, 给出了关于可估函数S\beta的线性估计在线性估计类中可容许性的充要条件Abstract: Consider the variance component model \ep Y=X\beta,\;\cov(Y)=\tsm_i=1^m\theta_iV_i, where X: n\times p and V_i\geq0\;(i=1,2,\cdots,m) are known, \beta\in R^p, \theta_i\geq0 or \theta_i>0 (i=1,2,\cdots,m) are parameters. In this paper, when \mu(X)\subset\mu(V), the sufficient and necessary conditions for a linear estimable estimator of S\beta to be admissible in the class of all linear estimators are given under quadratic loss function.
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