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This paper establishes asymptotic results for the maximum likelihood andrestricted maximum likelihood (REML) estimators of the parameters in the nestederror regression model for clustered data when both of the number ofindependent clusters and the cluster sizes (the number of observations in eachcluster) go to infinity. Under very mild conditions, the estimators are shownto be asymptotically normal with an elegantly structured covariance matrix.There are no restrictions on the rate at which the cluster size tends toinfinity 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 withincluster variance) differently from between cluster parameters (i.e.coefficients of cluster-level covariates that are constant within clusters andthe between cluster variance) because they require different normalisations andare asymptotically independent.

Increasing Cluster Size Asymptotics for Nested Error Regression Models