Admissible Estimators In Several Types Of Linear Models

Admissibility is one of the important criterions to compare the goodness of estimators in the view of the statistical decision. The theorem about the admissibility in the single linear model is comparative maturity, and includes integrated systemic results. In some widely applicable models, under matrix loss this paper studies the admissibility of linear estimators and gets some sufficient and necessary conditions about admissibility of estimators.We first state some basic theory about matrix and admissibility. And then, we introduce some conclusions about the admissibility of estimators in the single linear model. In the third chapter and forth chapter, we study admissible estimators in three types of linear models. 1. we study the admissibility of the linear estimator in a restricted multivariate linear model under matrix loss. We proof the fact that the admissibility of the linear estimator in a restricted multivariate linear model under matrix loss is identical with that of the linear estimator in the restricted single linear model under matrix loss. So we can generalize the conclusion of the linear estimator in the restricted single linear model to that of the linear estimator in a restricted multivariate linear model from. From that we can obtain the necessary and sufficient condition of admissible estimator of restricted multivariate linear model. 2. we study the admissibility of the linear estimator in a restricted growth curve model under matrix loss. We proof the fact that the admissibility of the linear estimator in a restricted growth curve model linear model under matrix loss is identical with that of the linear estimator in the restricted single linear model under matrix loss. From that we can easily obtain the necessary and sufficient conditions of admissible estimators in the homogeneous linear class. 3. we study admissibility of the multivariate stochastic linear model. Under the matrix loss function, the necessary and sufficient conditions that a simultaneous estimator of regression coefficient and parameters is admissible in the class of the homogeneous linear estimators are obtained in this paper.