摘要
本文在一些纯量损失和矩阵损失下研究带有结构变化的正态线性模型中参数的估计问题．分别给出 了存在回归系数的一致最小风险无偏（ＵＭＲＵ）估计和一致最小风险同变（ＵＭＲＥ）估计的充要条件， 证明了不存在误差方差在仿射变换群下的ＵＭＲＥ估计．导出了回归系数的最小二乘估计的可容许性 和极小极大性．
The problem of estimating parameters in a normal linear model with structural change under some scalar losses and matrix losses is studied. The necessary and sufficient exis- tence conditions aret respectively given for the uniformly minimum risk unbiased (UMRU) estimator and the uniformly minimum risk equivariant (UMRE) estimator of regression coef- ficients. It is proved that no UMRE estimators of error variances under an whne group exist. The admissibility and minimaxity of the least squares estimator of regression coefficients are also derived.
出处
《数学年刊（A辑）》
CSCD
北大核心
2001年第5期607-616,共10页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.19871088)
