二次损失下正态线性模型中可估函数的一切可容许估计(英文)  

All admissible linear estimators of estimable function in a normal linear model under quadratic loss

作　　者：胡桂开[1] 

机构地区：[1]东华理工大学理学院,江西南昌330013

出　　处：《安徽大学学报（自然科学版）》2013年第4期21-27,共7页Journal of Anhui University(Natural Science Edition)

基　　金：Supported by Youth Science Foundation of Educational Committee of Jiangxi Province(GJJ12388);Natural Science Foundation of Jiangxi Province(20122BAB211007);National Social Science Foundation of China(12BTJ014)

摘　　要：研究二次损失函数下正态线性模型中可估函数的齐次线性估计在一切估计类中的可容许性.对于非负定协方差矩阵和设计矩阵具有一定关系的正态线性模型,得到可估函数的约束齐次线性估计在一切估计类中可容许性的充分条件,并证明了在进一步的条件下,该充分条件也是此估计在一切估计类中可容许的必要条件.This article investigated the admissibility of linear estimators for estimable function in a normal linear model under quadratic loss function. A sufficient condition was given for restricted homogeneous linear estimators to be admissible in the space of all estimators when the nonnegative covariance matrix of the model was related to the design matrix. Furthermore, the sufficient condition was proved to be necessary if additional conditions were assumed.

关 键 词：二次损失 正态线性模型 可容许估计 

分 类 号：O212[理学—概率论与数理统计]