Small Areas, Benchmarking, and Political Battles: Today's Novel Demands in Small-Area Estimation

• Activity Number: 346
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: International Society for Bayesian Analysis (ISBA)
• Author(s): Rebecca C. Steorts*+
• Companies: Carnegie Mellon University
• Keywords: hierarchical and empirical Bayes ; small area estimation ; benchmarking ; mean squared error ; parametric boostrap

Abstract

We motivate small area estimation from the 2012 MLB season, illustrating the concepts of borrowing strength and shrinkage. Furthermore, we illustrate the relevance of benchmarking today by highlighting its key uses across the board in government applications, public policy needs, and industry applications. However, we mainly intend to establish that current benchmarking procedures can and should be improved, and thus, we propose a general class of benchmarked Bayes estimators that can be expressed in the form of a Bayesian adjustment applicable to any estimator, linear or nonlinear, that achieves this goal precisely. Furthermore, we propose novel ideas for benchmarking not only a weighted mean but also a weighted variability. Finally, we determine the excess mean squared error (MSE) from constraining the estimates through benchmarking under an empirical Bayes model, and we compare our approximation to a proposed parametric bootstrap estimator of the MSE of the benchmarked EB estimator. We illustrate our methods using data from the Small Area Income and Poverty Estimates Program of the U.S. Census Bureau, and in a simulation study.