An Objective Stepwise Bayes Approach to Small Area Estimation

• Activity Number: 571
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Survey Research Methods Section
• Author(s): Yanping Qu*+ and Glen Meeden and Bo Zhang
• Companies: FDA and University of Minnesota and Oregon State University
• Keywords: small area estimation ; non-informative Bayes ; Constrained Dirichelet Posterior ; survey sampling

Abstract

Small area estimation is an important area in survey sampling because of the growing demand for better statistical inference for small areas in public or private surveys. Some traditional methods for small area problems borrow strength through linear models that provide links to related areas, which may not be appropriate for some survey data. We propose a stepwise Bayes approach which borrows strength through an objective posterior distribution. This approach results in a generalized constrained Dirichlet posterior estimator when auxiliary information is available for small areas. The objective posterior distribution is based only on the assumption of exchangeability across related areas and does not make any explicit model assumptions. The form of our posterior distribution allows us to assign a weight to each member of the sample. These weights can then be used in a straight forward fashion to make inferences about the small area means. Numerically, we demonstrate in simulations and applications that the proposed stepwise Bayes approach can have substantial strengths compared to traditional methods.