Statistica Sinica 27 (2017), 1101-1123
Abstract: The nested error regression model is a useful tool for analyzing clustered (grouped) data, especially so in small area estimation. The classical nested error regression model assumes normality of random effects and error terms, and homoscedastic variances. These assumptions are often violated in applications and more exible models are required. This article proposes a nested error regression model with heteroscedastic variances, where the normality for the underlying distributions is not assumed. We propose the structure of heteroscedastic variances by using some specified variance functions and some covariates with unknown parameters. Under this setting, we construct moment-type estimators of model parameters and some asymptotic properties including asymptotic biases and variances are derived. For predicting linear quantities, including random effects, we suggest the empirical best linear unbiased predictors, and the second-order unbiased estimators of mean squared errors are derived in closed form. We investigate the proposed method with simulation and empirical studies.
Key words and phrases: Empirical best linear unbiased predictor, heteroscedastic variance, mean squared error, nested error regression, small area estimation, variance function.