Study On Parameter Estimation In A Mixed Model

The parameter estimation and its property are the focus of the linear model theory. In this dissertation, we mainly study on the parameter estimation in a mixed model. In term of the approximate multicollinearity of matrix, we propose the partial root root estimator and conditional partial root root estimator of coefficient in the classic linear model. The dissertation consists of the following parts:In the first chapter, we introduce the mixed model and its background. And introduce the majar work in this dissertation.In the second chapter, we consider the problem of estimating the regression coefficients in a mixed model under spherical constraints and ellipsoidal constraints.The minimax estimator is compared to classical regression. Sufficient conditions of this estimator have also been derived.In the third chapter, we study mixed estimator of regression coefficients under prior information and compare it with least square estimator(LSE). The upper and lower bounds of three new relative efficiency are obtained.In the forth chapter, we consider the mixed model under prior information and obtain parameter estimation subject to linear inequality. Then discusses its properties, such as MSEM-superiority, MSE-superiority comparisons between the new estimation and mixed estimation.In the fifth chapter, in term of the approximate multicollinearity of matrix, we propose the partial root root estimator of coefficient in the classic linear model and the conditional partial root root estimator of coefficient in the ristricted linear model. Under the mean square error matrix(MSE-M) criterion and Pitman Closeness(PC) criterion,the partial root root estimator and the conditional partial root root estimator are compared with LS estimator and RLS estimator respectively. And the superiority is achieved.