Estimation of Probability Density Function Under Judgment Post-Stratification Sampling Using Bayesian Estimation of Bandwidth

Abstract

Judgment Post-Stratification (JPS) is a sampling method that uses extra rank information in a simple random sampling (SRS) to stratify the sample and increase the efficiency of the estimators of the population parameters. In this paper, we consider the kernel estimation of the probability density function (pdf) using JPS sample. The properties of JPS estimator of pdf and the asymptotic mean integrated squared error of this estimator are obtained. We find a condition which guarantees that JPS density estimate performs better than its simple random sampling counterpart. To implement the kernel density estimator, it is required to specify a bandwidth. We use a Bayesian approach to find an estimate of the bandwidth. To compare the JPS density estimator with SRS estimator and also Bayesian bandwidth with other existing bandwidths, we use an extensive simulation study. Results are applied to the bone mineral density (BMD) data from the third National Health and Nutrition Examination Survey to estimate pdf of BMD.