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

In this paper, we propose a set of new mean estimators for judgment 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. (Ranked set sampling: theory and applications, Springer, New York, 2006).