Parameter Estimation And Testing Issues In Linear Mixed Model

This thesis briefly describes the form of linear mixed model analysis, studiesthe significance of variance, different methods of analysis of variance, and analyzesthe advantages and disadvantages of various parameter estimation methods underdifferent circumstances. By example, introduction the steps of variance analysis:formulating hypotheses; construct the test statistic; statistical decision. For thevariance component model, this thesis inducts the probability of a negative value ofANOVA estimation, the nature of the second unchanged estimation, the equalconditions of second invariant estimation and ANOVA estimation; improves thequadratic constant estimates to make it non-negative and outshine the ANOVAestimation and the minimum mean square error estimation; expands the scope of thecoefficient to construct a new class of unbiased estimations based on the secondunchanged estimate, improves the obtained class of non-negative estimation underquadratic loss. This thesis summarizes the nature of the generalized spectraldecomposition estimation and gives equal conditions of generalized spectraldecomposition estimation and ANOVA estimation. And studys the estimation ofvariance components which obtained by different analysis of variance in the linearmixed model with two and three variance components.In the mixed linear model with two variance components, there is censoredestimation of two variance component which are dominate the ANOVA estimationand the Tatsuya estimation in the mean-squared errors. For one-way classificationmodel to explore the estimation of estimated class which consistency better thanmaximum likelihood estimation and ANOVA estimation in the mean square errorsense; Obtaining quadratic invariant estimates, generalized spectral decompositionestimation and variance analysis estimation are equal in single error componentmodel and all of them are UMVUE. Given F test of variance components.To Mixed linear model with three variance components, this thesis discusseshow to get the components of variance estimation through spectral decompositionand improve the estimation of variance components in the mean-squared errors. To two stochastic models to classify for example, this thesis describes how to find thebeing censored estimation which better than the ANOVA estimates in the meansquare error. And describes an algorithm to reduce the amount of computation.