The Estimation Of Variance Component In Linear Mixed Model

Linear mixed model is an important branch of modern statistics. It is widely used in many areas of practical life. In particular, the research about parameter estimation becomes one of the front-burner issues. This thesis has mainly studied the estimation of variance component and the new definitions of the relative efficiency. Several new conclusions have been found.At first, taking different impacts of various dental fillings for instance, this thesis has analyzed longitudinal data model. And it has taken the PM2.5 which has an influence on respiratory system as example to account for variance component model. The transformation from special form to general type has been realized with variable substitution. Furthermore, this text has introduced the principle of minimum norm quadratic unbiased estimation after a comparison of various estimated methods, and explained maximum likelihood estimation(MLE) in detail. An optimal estimation of parameter in unbalanced one-way random effect model has been obtained based on the principle of MLE. Then a theorem has been derived for simplifying logarithm likelihood function to reduce computational complexity. And the restricted maximum likelihood estimation(REML) has made to revise MLE. Also, a case under extreme conditions has been given to illustrate the similarities and differences between them.To satisfy the Gauss-Markov assumption, the best linear unbiased estimation(BLUE) has been replaced by least square estimation(LSE). This replacement would bring loss. Thus relative efficiency has been put forward following measure these losses. For linear weighted regression model, two new relative efficie ncies have been defined after synthetic analysis of eight existing approaches. And their upper bounds are proved in this paper. Finally, this text gives a summary about validity and sensitivity of new relative efficiencies.