Parameter Estimation And Algorithm Research Of A Class Of Linear Mixed Model

The linear mixed model is a special linear model,which has unique advantages in dealing with repeated measurement data,interval data and spatial correlation data.In recent years,linear mixed models have been applied more and more widely in the fields such as biology,medicine,economics,finance,environmental science,sampling survey and engineering technology etc.Up to now,a large number of scholars pay more attention to its parameter estimation and property research,and have obtained relatively abundant result.The linear mixed model is mainly divided into two categories.One is the longitudinal model,which has independence between groups;the other is the variance component model,and its random effects are irrelevant.These two types of models can not cover each other in general.But one-way classification model,which has the advantage of two models we mentioned above,is the combination of longitudinal model and variance component model.In this thesis,we discuss the parameter estimation problem of one-way classification model and gain some result of this.The parameter estimation of the linear mixed model is divided into two main categories,one is the estimation of fixed effect and the other is the estimation of variance component.In this thesis,the fixed effect of three common linear mixed models is estimated by three different methods,i.e.the least squares estimate,two-step estimation and reduction estimation.With equilibrium data,the variance components of one-way classification model are estimated by analysis of variance estimate,maximum likelihood estimation,maximum likelihood estimation and minimum norm quadratic unbiased estimation.More than that,this thesis introduces the spectral decomposition estimation of the Panel data model and compares the result expressions of these estimates.Applying the maximum likelihood estimation,restricted maximum likelihood estimation and the minimum norm quadratic unbiased estimation to one-way classification model with the unbalanced data,and thus the linear equations are presented.Furthermore,the equation by iteration was solved by EM algorithm method,both from maximum likelihood estimation and limit maximum likelihood estimation.Finally,some comparison analysis between these two estimates was made by the programming tool,and get some important results is proposed.