Quantile Estimation for Judgement Post Stratification With an Application to Bone Mineral Density Study

Summary

In this paper, we deal with the problem of estimating the population quantiles using the judgement post stratification (JPS) sampling scheme. We introduce a general class of quantile function estimators, which includes quantile estimators based on both empirical and kernel distribution functions. We next study the asymptotic properties of the quantile estimators. Specifically, we prove that the estimators in the proposed class converge completely to the true quantile function under some mild conditions. We also establish the Bahadur representation for the JPS sample quantiles and address their multivariate normality. We then conduct an extensive Monte Carlo simulation study to compare the performance of the quantile function estimators in the JPS sampling design with their simple random sampling (SRS) competitors. Our study considers various factors such as sample size, set size, ranking quality, parent distribution and kernel function. Our findings show that the JPS estimators significantly enhance the efficiency of the quantile function estimators compared to their SRS counterparts across a broad range of scenarios. Finally, we illustrate the application of the proposed estimators to a real bone mineral density dataset from the Third National Health and Nutrition Examination Survey (NHANES III) to demonstrate their usefulness and practical benefits.