Proceedings of the Survey Methods Section SMALL AREA ESTIMATION USING ESTIMATED SAMPLING VARIANCES

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 variances are customarily assumed to be known in these models. In this paper we consider the situation where the sampling variances are estimated individually by direct estimators. A full hierarchical Bayes (HB) model is constructed for the direct survey estimators and the sampling variances estimators. We also consider the empirical best linear unbiased prediction (EBLUP) approach and obtain the EBLUP estimators. We compare the HB and the EBLUP methods through analysis of two survey data sets. Our results have shown that the proposed HB estimators perform better than the EBLUP estimators in terms of taking account of the extra uncertainty of estimating the sampling error variances, especially when the area-specific sample sizes are very small. When the sample sizes are large, both the HB and the EBLUP estimators perform equally better than the direct survey estimators in terms of coefficient of variation (CV) reduction. The proposed HB modeling approach will be applied to Canadian census undercoverage estimation and Canadian Labour Force Survey (LFS) unemployment and employment estimation