Wang Dewei, Tang Chuan-Fa, Tebbs Joshua M
Department of Statistics, University of South Carolina, Columbia, SC 29208, U.S.A.
Department of Mathematical Sciences, University of Texas-Dallas, Richardson, TX 75080, U.S.A.
Comput Stat Data Anal. 2020 Apr;144. doi: 10.1016/j.csda.2019.106898. Epub 2019 Dec 13.
The ordinal dominance curve (ODC) is a useful graphical tool to compare two population distributions. These distributions are said to satisfy uniform stochastic ordering (USO) if the ODC for them is star-shaped. A goodness-of-fit test for USO was recently proposed when both distributions are unknown. This test involves calculating the distance between an empirical estimator of the ODC and its least star-shaped majorant. The least favorable configuration of the two distributions was established so that proper critical values could be determined; i.e., to control the probability of type I error for all star-shaped ODCs. However, the use of these critical values can lead to a conservative test and minimal power to detect certain non-star-shaped alternatives. Two new methods for determining data-dependent critical values are proposed. Simulation is used to show both methods can provide substantial increases in power while still controlling the size of the distance-based test. The methods are also applied to a data set involving premature infants. An R package that implements all tests is provided.
序数优势曲线（ODC）是比较两个总体分布的一种有用的图形工具。如果它们的ODC是星形的，则称这些分布满足均匀随机序（USO）。最近有人提出了一种当两个分布都未知时对USO进行拟合优度检验的方法。该检验涉及计算ODC的经验估计值与其最小星形优超之间的距离。确定了两个分布的最不利配置，以便能够确定适当的临界值；即，控制所有星形ODC的I型错误概率。然而，使用这些临界值可能会导致检验保守，并且检测某些非星形备择假设的功效最小。提出了两种确定数据依赖临界值的新方法。通过模拟表明，这两种方法都可以在控制基于距离检验大小的同时大幅提高功效。这些方法也应用于一个涉及早产儿的数据集。提供了一个实现所有检验的R包。
