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 m...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 coefficientβin 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 ofβare 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 ofβ.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.10871146,10771015)
文摘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 coefficientβin 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 ofβare 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 ofβ.
