Estimations Of Variance Components In The Mixed Effects Models

This paper studies the problem of estimates of variance components in the mixed-effects model.The first chapter introduces the two models and its research status, and gives the required theoretical approaches in the article.The second chapter studies the problem of estimating variance components in the mixed model with one random effect, an improved class of combination estimation based on the quadratic statistics is acquired. An estimator in the improved class of estimation is achieved, which is better than ANOVAE under some simple conditions.Furthermore, a non-negative estimator is obtained, which has much smaller mean squared error comparing with ANOVAE under some conditions.The third chapter present the estimation of variance components matrix in multivariate linear mixed model with two variance components matrices. First, an improved class of estimate of variance component matrix of random effect in the mixed model is obtained. An estimator in the improved class of estimation is given, which is better than ANOVAE under a secondary risk. Furthermore, a better estimate is founded when a non-negative estimate having a smaller secondary risk does not exist,which has much smaller negative value and less risk than ANOVAE under some conditions.