Parameters Estimation In Mixed-Effect Models

Because the mixed-linear model is important in biology, medicines, economics, micro- computer, microwave engineering and other fields, so that the statisticians take more attention to the statistical research in this model. Concerning the estimation of the variance components, some estimators, for example, the Analysis of Variance Estimator (ANOVAE), Maximum Like- lihood Estimator (MLE), Restricted MLE, the minirnutn norm quadratic unbiased estimator (MINQUE), and so on, have been proposed in the literature. For these estimators, computation of the estimates of the fixed effect and the variance components are separated, and except of the ANONAE, they need solve a non-linear equations, unluckily, which do not have explicit solution, and only have an iteration solution in general. In this paper, on the basis of the decomposition of the covariance matrix, we l)roposed a new method that it can estimate the variance components and their fixed effect parameters simultaneously. This method has the following superiority over other estimators. Firstly, we can get several estimators of the fixed effect parameters, and these estimators do not contain the unknown parameters, i.e. these estimators are the feasible estimator, further, in some problems (see in the following example 1.3.1), those estimators have some good statistical properties. Secondly, we can use of the linear combination of these feasible estimators to get the generalized least squares estimator (GLSE) of the fixed effect parameters. And thirdly, on the basis of every feasible estimator, we can also get the estimates of the van- amice components only by solving a linear equations. Our research show that, in some models, especially in the mixed models with one variance components, the estimates of the fixed effect and the variance component obtained by our new method have good statistical properties, as far as the linear models contain more variance components, the statistical properties of the new method needs study deeply. In the rest of the paper, we apply the new method to some balance models, for example, mixed and random effect models, and compare the result with AVOVA estimate, we can observe that in those models, the results of the random models is same with the AVOVA, but in the mixed-effect models, the two-way crossed classification with interaction or no interaction, we get a different result frommm AVOVA estimate. In this paper, we also consider the unbiasedness of the two-stage estimate on basis of tIme estimates of variance components with time new tmmethod. For the general linear models, we also obtain the expression of the mean squared error of the two-stage estimator of regression coeffients.