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

Abstract

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.