Parameters Estimate For A Class Of Linear Mixed Models

Because of the wide usage of mixed model in biology, medicine and other fields, the statistic research on this model 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.Model with two variance components is common in linear mixed model. For the parameters of such model, the paper proposes a set of new estimates by singual alue decomposition theorem.For the fixed effects, the new estimate is linear estimate with good statistical properties. The paper give the sufficient condition of new estimate being the best linear unbiased estimate. The new estimate can be applied to models with three or more variance components.For the variance components, the new estimates have displayed solutions in a particular condition. When the loss function is square loss function, the paper gives a sufficient condition that the new estimates and Analysis of Variance Estimates achieve optimal; when the loss function is Stein loss function, the paper pointed out that the new estimates is better.