Prediction in Heteroscedastic Nested Error Regression Models with Random Dispersions

Abstract

The paper concerns small-area estimation in the heteroscedastic nested error regression (HNER) model which 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 samples sizes for small-areas. To fix this difficulty, 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 small sample sizes. Next we propose an empirical Bayes procedure 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 their second-order 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 the posted land price data.