Admissibilities of linear estimator in a class of linear models with a multivariate t error variable  

作　　者：YANG GuoQing 1 & WU QiGuang 2 1 Department of Mathematics,Tongji University,Shanghai 200092,China 2 Institute of Systems Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China 

出　　处：《Science China Mathematics》2010年第8期2011-2019,共9页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.10871146,10771015)

摘　　要：This paper discusses admissibilities of estimators in a class of linear models,which include the following common models:the univariate and multivariate linear models,the growth curve model,the extended growth curve model,the seemingly unrelated regression equations,the variance components model,and so on.It is proved that admissible estimators of functions of the regression coefficient β in the class of linear models with multivariate t error terms,called as Model II,are also ones in the case that error terms have multivariate normal distribution under a strictly convex loss function or a matrix loss function.It is also proved under Model II that the usual estimators of β are admissible for p 2 with a quadratic loss function,and are admissible for any p with a matrix loss function,where p is the dimension of β.This paper discusses admissibilities of estimators in a class of linear models,which include the following common models:the univariate and multivariate linear models,the growth curve model,the extended growth curve model,the seemingly unrelated regression equations,the variance components model,and so on.It is proved that admissible estimators of functions of the regression coefficient β in the class of linear models with multivariate t error terms,called as Model II,are also ones in the case that error terms have multivariate normal distribution under a strictly convex loss function or a matrix loss function.It is also proved under Model II that the usual estimators of β are admissible for p 2 with a quadratic loss function,and are admissible for any p with a matrix loss function,where p is the dimension of β.

关 键 词：MULTIVARIATE t distribution CONVEX LOSS QUADRATIC LOSS matrix LOSS ADMISSIBLE ESTIMATOR 

分 类 号：O211.67[理学—概率论与数理统计]