Asymptotic Analysis in Linear Mixed Effects Models With Large Cluster Size

Asymptotic results are considered for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model when both of 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.