Wang Dongliang, Hutson Alan D
Department of Public Health and Preventive Medicine, State University of New York Upstate Medical University, 750 East Adams Street, Syracuse, NY 13210, USA.
Department of Biostatistics, University at Buffalo, 3435 Main St., Buffalo, NY 14214-3000, USA.
J Appl Stat. 2013;40(3):614-625. doi: 10.1080/02664763.2012.750283.
Constructing confidence intervals (CIs) for a binomial proportion and the difference between two binomial proportions is a fundamental and well-studied problem with respect to the analysis of binary data. In this note, we propose a new bootstrap procedure to estimate the CIs by resampling from a newly developed smooth quantile function in [11] for discrete data. We perform a variety of simulation studies in order to illustrate the strong performance of our approach. The coverage probabilities of our CIs in the one-sample setting are superior than or comparable to other well-known approaches. The true utility of our new and novel approach is in the two-sample setting. For the difference of two proportions, our smooth bootstrap CIs provide better coverage probabilities almost uniformly over the interval (-1, 1), particularly in the tail region as compared than other published methods included in our simulation. We illustrate our methodology via an application to several different binary data sets.
对于二项比例以及两个二项比例之间的差异构建置信区间（CI），是二元数据分析中一个基础且研究充分的问题。在本笔记中，我们提出一种新的自助法程序，通过从[11]中为离散数据新开发的平滑分位数函数进行重采样来估计置信区间。我们进行了各种模拟研究，以说明我们方法的强大性能。在单样本设置中，我们的置信区间的覆盖概率优于或可与其他知名方法相媲美。我们新颖方法的真正效用体现在两样本设置中。对于两个比例的差异，我们的平滑自助置信区间几乎在区间（-1, 1）上一致地提供了更好的覆盖概率，特别是在尾部区域，与我们模拟中包含的其他已发表方法相比更是如此。我们通过应用于几个不同的二元数据集来说明我们的方法。
