The Estimators And Tests Of Variance Components In Longitudinal Data Model

Longitudinal data is referred to data in which the same individual is mea-sured repeatedly through dine. Many of statisticians have been interested inlongitudinal data at present. In this paper,we mainly study the estimators andtests of variance components in linear mixed model for longitudinal data.For the general linear mixed model with two variance components,theimproved combinatory spectral decomposition estimators of variance compo-nents are given. Under the normal assumptions,we study a class of invariantestimators. It is proved that there is no best estimator in the class under mean-squared-error criterion. In an important subclass,however,the best estimatoris obtained. At the same tine,we suggest the nonnegative estimator which isbetter than combinatory spectral decomposition estimator.Futhermore,this thesis studies nested error component balanced modelwith three variance components. As the methods Baltagi used to give theAnalysis of Variance(ANOVA)-type estimators-WH estimators,WK estima-tors,SA estimators, we get the corresponding estimators in nested error bal-anced model. What's more,we provide the improved estimators,especially aim-ing at the WK estimators of variance components of random effect and randomerror respectively, it is proved that the improved estimators we obtain are betterunder mean-squared-error criterion. In the last part of this paper,a procedure for testing variance componentsin linear mixed model with two variance components is developed. The testingis performed on the basis of a generalized p-value. We have first developedtests for a single random effect using the ideas of generalized p-value and gen-eralized confidence intervals. We have also developed similar procedures forobtaining the test for comparison of random effects in two models. The result-ing procedures are exact tests and easy to compute.