Empirical Bayes methods in nested error regression models with skew-normal errors

Abstract

The nested error regression (NER) model is a standard tool to analyze unit-level data in the field of small area estimation. Both random effects and error terms are assumed to be normally distributed in the standard NER model. However, in the case that asymmetry of distribution is observed in a given data, it is not appropriate to assume the normality. In this paper, we suggest the NER model with the error terms having skew-normal distributions. The Bayes estimator and the posterior variance are derived as simple forms. We also construct the estimators of the model-parameters based on the moment method. The resulting empirical Bayes (EB) estimator is assessed in terms of the conditional mean squared error, which can be estimated with second-order unbiasedness by parametric bootstrap methods. Through simulation and empirical studies, we compare the skew-normal model with the usual NER model and illustrate that the proposed model gives much more stable EB estimator when skewness is present.