SEVERAL RESULTS ON PARAMETER ESTIMATION IN SURE MODEL WITH SPECIAL COVARIANCE STRUCTURES
具有特殊协方差结构的 SURE 模型中参数估计的若干结果

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.