The Admissible Estimates Of The Parameter Of Linear Model

Linear model is one of the most important branches in Mathematical Statistics. Many subjects such as multivariate analysis, regression analysis, variance analysis and experiment design are either based on or have close relationship with linear model. As to statistical linear model, the basic problem is parameter estimation followed by further statistical analysis which depends on the estimation results. Though there exist various kinds of parameter estimators in literatures, it has always been an important research subject to measure the performance of these different estimators from the view of statistic decision, and the admissibility of parameter estimation is just one of the important statistical tools to solve such problem.This paper consists of four parts. The first is the part of introduction, in which we introduce the recent developments of admissible estimators and the main work we have done in this paper. Then we give some preliminary knowledge in the second part, including the concepts of some main risk functions and admissible estimators, which are needed in the following parts. In the third part, we give the admissible estimators of regression coefficients in statistical linear model with or without constraints. As to the linear model with equality constraints, we obtain the relationship between the homogeneous admissible estimators and the inhomogeneous admissible estimators. Finally, we have a discussion about the admissible estimators of the error variance in the fourth part. Now there are many results about the admissibility of the quadratic linear estimators, including both the homogeneous quadrics and the inhomogeneous quadrics. Some conclusions about the homogenous quadratic linear estimators could be found in [20][21]. In this paper, based on some changes of the model hypothesis in [20][21], we get the necessary condition under which the quadratic linear estimators are admissible.