Synthetic bias estimation in small area estimation

Small area estimation (SAE) has been one of the most active areas in survey methodology research, due to the increasing demand for small area statistics from government agencies and the private sector. But in some areas of interest, sample sizes could be very small, or even zero, in which case, "direct" estimates based on area-specific sample data may fail to provide estimates of adequate precision. It is common in these cases to use "indirect estimators", which use data from other areas. Many model-based small-area estimation methods have been proposed, including a simple and intuitive approach, "synthetic estimation". Synthetic estimates have smaller variances than direct estimates, but are usually biased. The bias is called synthetic estimation bias (SEB for short). An important application of synthetic estimation is in census coverage study.; The existing methods for SEB estimation in census coverage study context, include: (i) the unbiased estimator of SEB2 (the square of synthetic estimation bias), (ii) Marker's (1995) estimator of SEB 2, and (iii) surrogate variable methods. Each of these methods has drawbacks. Method (i) yields negative estimates of SEB2. Method (ii) estimates the SEB2 to be the same for each area, and method (iii) strongly depends on untested model assumptions. We propose the EB estimators of SEB and SEB2, which are based Hierarchical Bayes (HB) models, with carefully selected weight functions. Simulation studies indicate consistent improvement over the existing methods in many cases. We apply the "best" estimator identified by simulation studies to better understand the magnitude of SEB in the Census Bureau's estimates of net undercount in the 2000 census.; We develop model building procedures to construct hierarchical Bayes models for SEB estimation in census coverage study context. We derive the RMSE (Root MSE) for A.C.E. Revision II for Census 2000 by incorporating the estimated SEB2. We also investigate the degree of departure from synthetic model, by comparing the estimates of SEB2 at the LCO (local census office) level and the state level. Finally we study the impact of SEB estimation in loss function analysis related to whether census or adjustment should be used.