Bayesian Benchmarking with Applications to Small-Area Estimation

• Activity Number: 243
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Government Statistics
• Author(s): Rebecca Carter Steorts*+ and Ghosh Malay and Gauri Datta
• Companies: University of Florida and University of Florida and The University of Georgia
• Keywords: Area-level ; penalty parameter ; two-stage ; weighted mean ; weighted variability ; benchmarking

Abstract

Often in small area estimation model-based estimates differ widely from direct estimates, especially for areas with low sample sizes. While model-based estimates are useful, one difficulty with such estimates is that when aggregated, the overall estimate for a larger geographical area may be quite different from the corresponding direct estimate, the latter being usually believed to be quite reliable.

One way to avoid this is using benchmarking, where we modify the model-based estimates so that we get the same aggregate estimate for the larger geographical area. We propose a general class of constrained Bayes estimators which achieve the necessary benchmarking. Explicit Bayes estimators are derived which benchmark the weighted mean or both the weighted mean and weighted variability. We illustrate our methodology with an example using U.S. Census data.