Asymptotic Theory for Linear Mixed Effects Models With Large Cluster Size

Abstract

This thesis first deals with asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model when both the number of independent clusters and the cluster sizes (the number of observations in each cluster) go to infinity. A set of conditions is given under which the estimators are shown to be asymptotically normal. There are no restrictions on the rate at which the cluster size tends to infinity. Moreover, this thesis deals with the estimated distributions of the estimated best linear unbiased predictors (EBLUP) of the random effects, with ML/REML, estimated variance components, converge to the true distributions of the corresponding random effects, when both of the number of independent clusters and the cluster sizes (the number of observations in each cluster) go to infinity.