Bayesian Inference of Finite Population Distribution Functions and Quantiles from Unequal Probability Samples

• Activity Number: 357
• Type: Topic Contributed
• Date/Time: Tuesday, August 4, 2009 : 2:00 PM to 3:50 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Qixuan Chen*+ and Michael Elliott and Roderick J.A. Little
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: heteroscedastic error ; penalized spline ; probability-proportional-to-size ; multinomial probit regression ; survey samples

Abstract

This paper develops two robust Bayesian predictive estimators of finite population distribution functions and associated quantiles for continuous variables in the setting of unequal probability sampling, where inferences are based on the posterior predictive distribution of the non-sampled values. The first method fits a multinomial ordinal probit regression model of the distribution function evaluated at multiple values on a penalized spline of the selection probabilities. The second method is to posit a smoothly-varying relationship between the outcome and the selection probabilities by modeling both the mean function and the variance function using penalized splines. Simulation studies show that both methods yield estimators that are more efficient with closer to the nominal level credible intervals than the design-based estimators.