The Parameter Estimation Of Linear Mixed Model

Linear mixed model is widely used in biology, medicine, computer, microwave engi-neering and other fields. Statistic research on this model has received increasing attention. The unknown parameters of this model are divided into two categories:one is the fixed effects, and the other is the variance components. In this thesis, we mainly discuss pa-rameter estimation, nonnegative improvement, admissibility and relative problems. Some new results are obtained.Firstly, the covariance matrix of random effects in linear mixed model is extended to positive matrix. We construct the estimation of variance components based on the idea of ANOVA estimator. It is also showed that QR decomposition can reduce the amount of data in computation. Simultaneously, an improved estimation is obtained by the application of the covariance of quadratic forms of random variables. A nonnegative estimation of variance components is also given. In linear mixed model with two variance components, this thesis puts forward a class of the quadratic invariant estimators of the variance components, in which we discuss the necessary conditions of admissibility. On the basis of this new class, another estimator is obtained which is better than ANOVA estimator. In addition, in a linear unbiased class of estimators of sβ, the necessary condition of admissibility is derived. At last, we propose some meaningful questions to be solved.