Small area estimation under transformed nested-error regression models

The empirical best linear unbiased prediction (EBLUP) based on the nested error regression model (Battese et al. in J Am Stat Assoc 83:28–36, 1988, NER) has been widely used for small area mean estimation. Its so-called optimality largely depends on the normality of the corresponding area level and unit level error terms. To allow departure from normality, we propose a transformed NER model with an invertible transformation, and employ the maximum likelihood method to estimate the underlying parameters of the transformed NER model. Motivated by Duan’s (J Am Stat Assoc 78:605–610, 1983) smearing estimator, we propose two small area mean estimators depending on whether all the population covariates or only the population covariate means are available in addition to sample covariates. We conduct two design-based simulation studies to investigate their finite-sample performance. The simulation results indicate that compared with existing methods such as the empirical best linear unbiased prediction, the proposed estimators are nearly the same reliable when the NER model is valid and become more reliable in general when the NER model is violated. In particular, our method does benefit from incorporating auxiliary covariate information.