具有特殊协方差结构的 SURE 模型中参数估计的若干结果

本文讨论具有特殊协方差结构似乎不相关回归方程（SURE）模型中参数的估计问题．除非另有说明，损失函数将取为二次损失和矩阵损失．本文证明了回归系数的线性可估函数的最小二乘估计是极小极大的且在矩阵损失函数下是可容许的；还分别在仿射交换群和平移群下导出了存在回归系数的线性可估函数的一致最小风险同变（UMRE）估计的充要条件，并证明了在仿射交换和二次损失下不存在协方差阵和方差的UMRE估计．

SEVERAL RESULTS ON PARAMETER ESTIMATION IN SURE MODEL WITH SPECIAL COVARIANCE STRUCTURES

This paper discusses the problem of estimating parameters in seemingly unrelated regression equations (SURE) model with special covariance structures. The loss functions are taken to be quadratic loss and matrix loss unless otherwise stated. It is proved that the least square estimators of linear estimable functions of regression coefficients are admissible under matrix loss and minimax. The necessary and sufficient existence conditions are derived for the uniformly minimum risk equivariant (UMRE) estimators of linear estimable functions of regression coefficients under an affine group and a transitive group of transformations respectively. It is also proved that there are no UMRE estimators of the covariance matrix and variance under an affine group of transformations and quadratic loss functions.