Bayesian nonparametric estimation of finite population quantities in absence of design information on nonsampled units

In Probability proportional to size (PPS) sampling, the sizes for nonsampled units are not required for the usual Horvitz-Thompson or Hajek estimates, and this information is rarely included in public use data files. Previous studies have shown that incorporating information on the sizes of the nonsampled units through semiparamteric models can result in improved estimates. When the design variables that govern the selection mechanism, are missing, the sample design becomes informative and predictions need to be adjusted for the effect of selection. We present a general framework using Bayesian nonparametric mixture modeling with Dirichlet process priors for imputing the nonsampled size variables, when such information is not available to the statistician analyzing the data.