In this paper, we introduce two robust, nonparametric methods for multiple change-point detection in the variability of a multivariate sequence of observations. We demonstrate that changes in ranks generated from data depth functions can be used to detect changes in the variability of a sequence of multivariate observations. In order to detect more than one change, the first algorithm uses methods similar to that of wild-binary segmentation. The second algorithm estimates change-points by maximizing a penalized version of the classical Kruskal Wallis ANOVA test statistic. We show that this objective function can be maximized via the well-known PELT algorithm. Under mild, nonparametric assumptions both of these algorithms are shown to be consistent for the correct number of change-points and the correct location(s) of the change-point(s). We demonstrate the efficacy of these methods with a simulation study, where we compare our new methods to several competing methods. We show our methods outperform existing methods in this problem setting, and our methods can estimate changes accurately when the data are heavy tailed or skewed.
翻译:在本文中,我们引入了两种强健的非参数方法,用于在多变量观测序列的变异性中进行多点多变检测。我们证明,数据深度函数产生的等级变化可用于检测多变量观测序列变异性的变化。为了检测不止一个变化,第一种算法使用了类似于野生二元分离的方法。第二种算法通过最大限度地增加经典Kruskal Wallis ANOVA测试统计数据的受罚版本来估计变化点。我们显示,通过众所周知的PELT算法,可以最大限度地发挥这一客观功能。在轻度、非参数假设下,这两种算法对于变化点的正确数量和变化点的正确位置都是一致的。我们用模拟研究来展示这些方法的功效,我们用模拟研究将新方法与几种相竞方法进行比较。我们展示了我们的方法超越了这一问题设置中的现有方法,我们的方法可以精确地估计数据严重尾部或扭曲时的变化。