A Further Study Of Linear Mixed Models

Linear mixed model is a special kind of linear models. Also, it is the furtherdevelopment and extension of the linear regression model. This model which has got agreat development in recent decades can be used to deal with complex data with nestedstructure. This paper mainly concerned with the prediction problems in linear mixedmodel and a perfect theory system about the prediction of mixed effects is established.Some commonly used estimation methods of variance components are introduced.There are mainly two aspects to study, i.e., the prediction of mixed effects and theestimation of variance components. In Chapter2, we promote the best linear unbiasedpredictor which always plays the central role. The unified theory of the prediction ofmixed effects is established including the fitting of response variables and the predictionof response variables in the new data. As applications, we propose ridge predictor,mixed predictor and restricted ridge predictor in Chapter3. The performance of the newpredictors can be examined easily with the help of vast literature on the linearregression model. We also illustrate our findings with a Monte Carlo simulation and anumerical example. In Chapter4, we mainly introduce some usual methods to estimatethe unknown variance components.The prediction theory of the mixed effects in this paper establishes on the base oflinear regression model. Many other predictors can be proposed by the same way withthe help of research results of linear regression model. The statistical inference of thepredictors and the combination with the estimation of variance components will be theemphasis and difficulty.