Wang Xinlei, Lim Johan, Stokes Lynne
Department of Statistical Science, Southern Methodist University, 3225 Daniel Avenue, P.O. Box 750332, Dallas, Texas 75275-0332, USA.
Biometrics. 2008 Jun;64(2):355-63. doi: 10.1111/j.1541-0420.2007.00900.x. Epub 2008 Mar 5.
MacEachern, Stasny, and Wolfe (2004, Biometrics60, 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.
麦克埃彻恩、斯塔斯尼和沃尔夫（2004年，《生物统计学》60卷，207 - 215页）引入了一种数据收集方法，称为判断后分层（JPS），其基于与秩集抽样中类似的思想，并提出了从JPS样本进行均值估计的方法。在本文中，我们对他们的方法提出一种改进，该改进利用了判断后分层的分布通常按随机顺序排列这一事实，以便使用后分层的等距样本均值形成一个均值估计量。这个新的估计量具有强一致性，其渐近性质与麦克埃彻恩等人（2004年）的类似。结果表明，对于小样本量，它更有效，这在需要成本效益的应用中似乎很有吸引力。此外，我们将我们的方法扩展到具有不精确排序或多个排序者的JPS样本。通过模拟在三个数据示例上检验了所提出估计量的性能。
