Pauly Markus, Asendorf Thomas, Konietschke Frank
Institute of Statistics, University of Ulm, Helmholtzstrasse 20, 89081, Ulm, Germany.
Department of Medical Statistics, University of Goettingen, Humboldtallee 32, 37073, Goettingen, Germany.
Biom J. 2016 Nov;58(6):1319-1337. doi: 10.1002/bimj.201500105. Epub 2016 Aug 9.
We investigate rank-based studentized permutation methods for the nonparametric Behrens-Fisher problem, that is, inference methods for the area under the ROC curve. We hereby prove that the studentized permutation distribution of the Brunner-Munzel rank statistic is asymptotically standard normal, even under the alternative. Thus, incidentally providing the hitherto missing theoretical foundation for the Neubert and Brunner studentized permutation test. In particular, we do not only show its consistency, but also that confidence intervals for the underlying treatment effects can be computed by inverting this permutation test. In addition, we derive permutation-based range-preserving confidence intervals. Extensive simulation studies show that the permutation-based confidence intervals appear to maintain the preassigned coverage probability quite accurately (even for rather small sample sizes). For a convenient application of the proposed methods, a freely available software package for the statistical software R has been developed. A real data example illustrates the application.
我们研究了用于非参数贝伦-费希尔问题（即ROC曲线下面积的推断方法）的基于秩的学生化置换方法。在此，我们证明了布鲁纳-蒙泽尔秩统计量的学生化置换分布即使在备择假设下也渐近于标准正态分布。因此，顺便为诺伊伯特和布鲁纳学生化置换检验提供了迄今缺失的理论基础。特别是，我们不仅证明了其一致性，还表明可以通过对该置换检验求逆来计算潜在治疗效果的置信区间。此外，我们推导了基于置换的范围保持置信区间。大量的模拟研究表明，基于置换的置信区间似乎能相当准确地保持预先指定的覆盖概率（即使对于相当小的样本量也是如此）。为方便应用所提出的方法，我们开发了一个可免费获取的用于统计软件R的软件包。一个实际数据示例说明了该应用。
