Bayesian Inference for the Finite Population Total from a Heteroscedastic Probability Proportional to Size Sample

• Activity Number: 16
• Type: Topic Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Sahar Zangeneh*+ and Roderick Little
• Companies: University of Michigan and University of Michigan/U.S. Census Bureau
• Keywords: Bayesian bootstrap ; Heteroscedasticity ; Penalized spline ; Probability proportional to size ; Metropolis-Hastings within Gibbs

Abstract

We study Bayesian inference for the finite population total (T) in probability proportional to size (PPS) sampling. The sizes of nonsampled (NS) units are not required for the usual Horvitz-Thompson (HT) or Hajek estimates, and this information is rarely included in public use data files. Zheng and Little (JOS 2003) showed that including the sizes of the NS units as predictors in a spline model can result in improved point estimates of T, and later combine this with a Bayesian bootstrap (BB) model for the sizes, when they are only known for the sampled units. We further develop their methods by (a) including an unknown parameter to model heteroscedastic error variance in the spline model, an important modeling feature in the PPS setting; and (b) developing an improved Bayesian method for including summary information about the aggregate size of NS units. Simulation studies suggest that t