Bayesian Penalized Spline Model-Based Estimation of the Finite Population Proportion From Probability-Proportional-to-Size Samples

This paper develops Bayesian penalized spline predictive (BPSP) estimator of finite population proportion for probability-proportional-to-size samples. This new method allows the probabilities of inclusion to be directly incorporated into the estimation of population proportion, using a probit regression of the binary outcome on the penalized spline of the inclusion probabilities. The posterior distribution of the population proportion is then obtained using Gibbs sampling. Simulation studies show that the BPSP estimator gains efficiency over the HT estimator by using the inclusion probabilities in the nonsampled units, and that the BPSP estimator has a better coverage with narrower credible interval over the HT estimator, especially when the true population proportion is close to zero or one for small samples.