Small area estimation using area level models and estimated sampling variances - ARCHIVED

In small area estimation, area level models such as the Fay - Herriot model (Fay and Herriot 1979) are widely used to obtain efficient model-based estimators for small areas. The sampling error variances are customarily assumed to be known in the model. In this paper we consider the situation where the sampling error variances are estimated individually by direct estimators. A full hierarchical Bayes (HB) model is constructed for the direct survey estimators and the sampling error variances estimators. The Gibbs sampling method is employed to obtain the small area HB estimators. The proposed HB approach automatically takes account of the extra uncertainty of estimating the sampling error variances, especially when the area-specific sample sizes are small. We compare the proposed HB model with the Fay - Herriot model through analysis of two survey data sets. Our results have shown that the proposed HB estimators perform quite well compared to the direct estimates. We also discussed the problem of priors on the variance components.