The nested error regression model is a useful tool for analyzing clustered(grouped) data, and is especially used in small area estimation. The classicalnested error regression model assumes normality of random effects and errorterms, and homoscedastic variances. However, these assumptions are oftenviolated in real applications and more flexible models are required. Thisarticle proposes a nested error regression model with heteroscedasticvariances, where the normality for the underlying distributions is not assumed.We propose the structure of heteroscedastic variances by using some specifiedvariance functions and some covariates with unknown parameters. Under thesetting, we construct the moment-type estimators of model parameters and someasymptotic properties including asymptotic biases and variances are derived.For predicting linear quantities including random effects, we suggest theempirical best linear unbiased predictors and the second-order unbiasedestimators of mean squared errors are derived in the closed form. Weinvestigate the proposed method with simulation and empirical studies.
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