Empirical Bayes and hierarchical Bayes estimation of small area characteristics

The sampling designs of the national surveys are usually determined so as to produce reliable estimates of various characteristics at the national level. The direct survey estimates, however, perform poorly at the subnational regions (e.g., state, county, etc.) due to small sample sizes available from the respective regions. Such a problem is known as small area estimation in survey sampling literature. Different hierarchical Bayes (HB) and empirical Bayes (EB) estimators are proposed to estimate small area characteristics. The results are also applicable to repeated surveys where the physical characteristics of the sampling units change slowly over time. The hierarchical models used to generate EB and HB estimators borrow strength from the related resources. Two survey situations are considered. In the first situation, samples are drawn from finite populations of known sizes using stratified random design. In the second situation, information about the sampling design is available only through sampling weights, determined using different factors such as inclusion probabilities, poststratification, nonresponse etc. The proposed EB and HB estimators perform better than the direct survey estimators both for large and small samples. The Bayes and the EB estimators are shown to be superior to the BLUP under a mixed model with random variance component