Statistica Sinica 26 (2016), 465-492 doi:http://dx.doi.org/10.5705/ss.202014.0070
Abstract: The paper considers small-area estimation for a heteroscedastic nested error regression (HNER) model that assumes that the within-area variances are different among areas. Although HNER is useful for analyzing data where the within-area variation changes from area to area, it is difficult to provide good estimates for the error variances because of small sample sizes for small-areas. To address this issue, we suggest a random dispersion HNER model which assumes a prior distribution for the error variances. The resulting Bayes estimates of small area means provide stable shrinkage estimates even for areas with small sample sizes. Next we propose an empirical Bayes approach for estimating the small area means. For measuring uncertainty of the empirical Bayes estimators, we use the conditional and unconditional mean squared errors (MSE) and derive second-order correct approximations. It is interesting to note that the difference between the two MSEs appears in the first-order terms while the difference appears in the second-order terms for classical normal linear mixed models. Second-order unbiased estimators of the two MSEs are given with an application to posted land price data. Also, some simulation results are provided.
Key words and phrases: Asymptotic approximation, conditional mean squared error, empirical Bayes, parametric bootstrap, second-order approximation, second-order unbiased estimate, small area estimation.