Prediction of the nonsampled units in survey design with the finite population using Bayesian nonparametric mixture model

Abstract

In the sampling approaches framework, the combination of the information on the sizes of the nonsampled units can help to attain better estimators by using semiparametric models. Sometimes, the design variables that have an important role in the sampling mechanism are not available. Hence predictions require to be adapted for the consequence of selection. To infer the population mean in a sample survey, we study Bayesian nonparametric model with Dirichlet process prior by considering the inverse-probability weights as the only available information. Indeed, we present a Bayesian nonparametric mixture of regression models for the survey outcomes with the weights as predictors and impute the nonsampled units. Finally, the model-based estimators that are derived from the Bayesian (parametric and nonparametric) methods are compared with the design-based estimator based on the simulation approaches.

Keywords:

• Bayesian nonparametric
• Dirichlet Process
• Nonparametric regression model
• Poststratification
• Sample survey inference
• Survey weighting