Proceedings of the Survey Methods Section BENCHMARKING HIERARCHICAL BAYES SMALL AREA ESTIMATORS WITH APPLICATION IN CENSUS UNDERCOVERAGE ESTIMATION

Linear mixed effects models such as the Fay-Herriot model (1979) and non-linear mixed effects models such as the unmatched area level models proposed by You and Rao (2002) have been used in small area estimation to obtain efficient model-based small area estimators. It is often desirable to benchmark the model-based estimates so that they add up to the direct survey estimates for large areas to protect against possible model mis-specification and possible overshrinkage. In this paper, hierarchical Bayes (HB) unmatched area level models are considered. Posterior means and posterior variances of parameters of interest are first obtained using the Gibbs sampling method. Then we benchmark the HB estimators (posterior means) to obtain the benchmarked HB (BHB) estimators. Posterior mean squared error (PMSE) is then used as a measure of uncertainty for the BHB estimators. The PMSE can be represented as the sum of the usual posterior variance and a bias correction term. We evaluate the HB and the BHB estimators in the application of Canadian census undercoverage estimation. The sum of the provincial BHB census undercount estimates is equal to the direct survey estimate of the census undercount for the whole nation