Bayesian Benchmarking with Applications to Small Area Estimation

• Activity Number: 246
• Type: Invited
• Date/Time: Tuesday, August 4, 2009 : 8:30 AM to 10:20 AM
• Sponsor: International Indian Statistical Association
• Author(s): Gauri S. Datta*+ and Malay Ghosh and Rebecca Steorts and Jerry J. Maples
• Companies: The University of Georgia and University of Florida and University of Florida and U.S. Census Bureau
• Keywords: Area-level ; penalty parameter ; two-stage ; weighted mean ; weighted variability

Abstract

Popular model-based small area estimates face a problem that when aggregated over a larger domain, the result may not agree with the direct estimate. The latter is felt reliable as a survey is designed for better accuracy at larger domain. While an agreement with an aggregated direct estimate at some level protects against model failure, it is often politically necessary to convince the utility of small area estimates. For an agreement benchmarking is used to modify the model-based estimates. Raking, popular in benchmarking, scales the small area estimates by a factor so that two weighted totals agree. It is used for convenience with no firm statistical principle and it has some deficiency. We use constrained Bayes estimators that benchmark the weighted mean, or the weighted mean and variability. Interestingly, many frequentist solutions including raking are special cases of our result.