A Nonparametric Mean Estimator for Judgment Post-Stratified Data

• Activity Number: 499
• Type: Topic Contributed
• Date/Time: Thursday, August 2, 2007 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Xinlei Wang*+ and Johan Lim and S. Lynne Stokes
• Companies: Southern Methodist University and Yonsei University and Southern Methodist University
• Keywords: Imperfect Ranking ; Imprecise Ranking ; Isotonic Regression ; Multiple Rankers ; Ranked Set Sampling ; Simple Stochastic Ordering

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 et al. (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.