Bayesian Nonparametric Joint Model for Point Estimates and Variances under Biased Domain Variances

• Activity Number: 503 - Small Area Estimation with Relaxed Modeling Assumptions
• Type: Topic Contributed
• Date/Time: Wednesday, July 31, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Survey Research Methods Section
• Author(s): Julie Gershunskaya* and Terrance Savitsky
• Companies: U.S. Bureau of Labor Statistics and Bureau of Labor Statistics
• Keywords: Bayesian Hierarchical Modeling; Dirichlet process; Variational Bayes; Stan; Weight smoothing

Abstract

We propose a joint model for point estimates and their variances when observed variances may contain bias. The bias in variances for groups of domains may be induced by an estimation procedure, such the weight smoothing procedure of Beaumont (2008) to compute a domain point estimator. While the weight-smoothed point estimator is more efficient than the original weighted survey estimator, its variance estimation procedure requires truncations that induces bias in the domain variance estimator. The proposed formulation generalizes the joint point estimator and variance models to explicitly parameterize a multiplicative bias in observed variances under a nonparametric formulation that allows the data to discover distinct bias regimes. As a consequence of the better variance estimation, domain point estimates are more robustly estimated under a joint model for the domain point estimates and their associated variances. We compare the performances of alternative models in application to estimates from the Current Employment Statistics survey and in simulations.