Increasing cluster size asymptotics for nested error regression models

This paper establishes asymptotic results for the maximum likelihood and restricted (REML) estimators of parameters in nested error regression model clustered data when both number independent clusters cluster sizes (the observations each cluster) go to infinity. Under very mild conditions, are shown be asymptotically normal with an elegantly structured covariance matrix. There no restrictions on rate at which size tends infinity but it turns out that we need treat within (i.e. coefficients unit-level covariates vary variance) differently from between cluster-level constant because they require different normalisations independent. • Central limit theorem ML REML estimates models. Results allow increase. Detailed comparison fixed results. Derive standard errors (including variance components) under frameworks. Study simulation performance confidence intervals