论文标题
使用数据深度的多元变异性可稳健多个更改点检测
Robust multiple change-point detection for multivariate variability using data depth
论文作者
论文摘要
在本文中，我们引入了两种健壮的非参数方法，用于在多元观测值序列的可变性中进行多个更改点检测。我们证明，从数据深度函数产生的等级的变化可用于检测一系列多变量观察序列变化的变化。为了检测多次变化，第一个算法使用类似于野生二进制分割的方法。第二种算法通过最大化经典的Kruskal Wallis ANOVA测试统计量的惩罚版本来估算变化点。我们表明，该目标函数可以通过众所周知的PELT算法最大化。在轻度的，非参数假设下，这两种算法都证明对正确数量的更改点和更改点的正确位置是一致的。我们通过模拟研究证明了这些方法的功效，在该研究中，我们将新方法与几种竞争方法进行了比较。我们显示我们的方法在此问题设置中的表现优于现有方法，并且当数据沉重或偏斜时，我们的方法可以准确估算更改。
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.
