A Bayesian benchmarking of the Scott–Smith model for small areas

Abstract

When the finite population ‘totals’ are estimated for individual areas, they do not necessarily add up to the known ‘total’ for all areas. Benchmarking (BM) is a technique used to ensure that the totals for all areas match the grand total, which can be obtained from an independent source. BM is desirable to practitioners of survey sampling. BM shifts the small-area estimators to accommodate the constraint. In doing so, it can provide increased precision to the small-area estimators of the finite population means or totals. The Scott–Smith model is used to benchmark the finite population means of small areas. This is a one-way random effects model for a superpopulation, and it is computationally convenient to use a Bayesian approach. We illustrate our method by estimating body mass index using data in the third National Health and Nutrition Examination Survey. Several properties of the benchmarked small-area estimators are obtained using a simulation study.