This paper establishes asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model for clustered data when both of the number of independent clusters and the cluster sizes (the number of observations in each cluster) go to infinity. Under very mild conditions, the estimators are shown to be asymptotically normal with an elegantly structured covariance matrix. There are no restrictions on the rate at which the cluster size tends to infinity but it turns out that we need to treat within cluster parameters (i.e. coefficients of unit-level covariates that vary within clusters and the within cluster variance) differently from between cluster parameters (i.e. coefficients of cluster-level covariates that are constant within clusters and the between cluster variance) because they require different normalisations and are asymptotically independent.

本文建立了聚类数据的嵌套误差回归模型中参数的最大似然和受限最大似然（REML）估计量的渐近结果，当独立簇数和簇大小（每个簇中的观察数）去无穷大。在非常温和的条件下，估计量显示为具有优雅结构的协方差矩阵渐近正态。对集群大小趋于无穷大的速率没有限制，但事实证明，我们需要对集群内参数（即在集群内变化的单位级协变量的系数和集群内方差）与集群参数之间进行不同的处理（IE