Statistical Science Department Seminar

April 18, 2008

An Efficient Nonparametric Estimator for Judgment Post-Stratified Data

Sherry Wang, SMU

Abstract 

MacEachern, Stasny and Wolfe (2004) introduced a data collection method, called judgment post-stratification (JP-S), based on ideas similar to those in ranked set sampling, and proposed methods for mean estimation from JP-S samples. In this paper we propose an improvement to their methods, which exploits the fact that the distributions of the judgment post-strata are often stochastically ordered, so as to form a mean estimator using isotonized sample means of the post-strata. This new estimator is strongly consistent with similar asymptotic properties to those in MacEachern, Stasny and Wolfe (2004). It is shown to be more efficient for small sample sizes, which appears to be attractive in applications requiring cost efficiency. Further, we extend our method to JP-S samples with imprecise ranking or multiple rankers. The performance of the proposed estimators is examined on three data examples through simulation.