A nonparametric mean estimator for judgment poststratified data |
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Authors: | Wang Xinlei Lim Johan Stokes Lynne |
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Institution: | Department of Statistical Science, Southern Methodist University, 3225 Daniel Avenue, P.O. Box 750332, Dallas, Texas 75275-0332, U.S.A.;Department of Applied Statistics, Yonsei University, Seoul 120-749, Korea |
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Abstract: | Summary . MacEachern, Stasny, and Wolfe (2004, Biometrics 60 , 207–215) introduced a data collection method, called judgment poststratification (JPS), based on ideas similar to those in ranked set sampling, and proposed methods for mean estimation from JPS samples. In this article, we propose an improvement to their methods, which exploits the fact that the distributions of the judgment poststrata are often stochastically ordered, so as to form a mean estimator using isotonized sample means of the poststrata. 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 JPS samples with imprecise ranking or multiple rankers. The performance of the proposed estimators is examined on three data examples through simulation. |
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Keywords: | Imperfect ranking Imprecise ranking Isotonic regression Multiple rankers Ranked set sampling Simple stochastic ordering |
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