Generalized Isotonized Mean Estimators for Judgment Post-Stratification with Multiple Rankers

• Activity Number: 494
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Marketing
• Author(s): Min Chen*+ and Johan Lim and Xinlei Wang and Johan Lim
• Companies: University of Texas at Dallas and Seoul National University and Southern Methodist University and Seoul National University
• Keywords: best linear unbiased estimator ; generalized isotonic regression ; matrix partial order ; simple stochastic order ; ranked set sampling ; raking

Abstract

We propose a new set of mean estimators for judgement post-stratified data with multiple rankers. The new estimators take into account matrix partial ordering in cumulative distribution functions of rank strata, and they are derived by improving existing estimators through employing the order constraints and solving a generalized isotonic regression problem. Numerical studies show that the proposed isotonized mean estimators outperform the existing estimators. Finally, the proposed estimators are applied to estimating the average tree height using the tree data in Chen et al. (2006).