Isotonic Mean Estimator for the Judgement-Post Stratified Samples

• Activity Number: 280
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Johan Lim*+ and Soohyun Ahn and Sherry Wang and Min Chen
• Companies: Seoul National University and Seoul National University and Southern Methodist University and The University of Texas Southwestern Medical Center at Dallas
• Keywords: Isotonic Regression ; Judgement Post-Stratification ; Multiple ranker ; Stochastic Order

Abstract

MacEachern, Stasny, and Wolfe (2004, Biometrics60, 207-215) introduced a data collection method, called judgment post-stratification (JPS), based on ideas similar to those in ranked set sampling, and proposed methods for mean estimation from JPS samples. 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. In this work, we further extend our method to JPS samples with multiple rankers. The new estimator for the JPS with multiple rankers solve the generalized isotonic regression with matrix partial order. The performance of the new estimator is compared to other existing estimators through simulation.