Robust multiple change-point detection for multivariate variability using data depth

TL;DR

This paper proposes two robust, nonparametric methods for detecting multiple change-points in multivariate data variability using data depth functions, outperforming existing methods especially with heavy-tailed or skewed data.

Contribution

Introduces two novel nonparametric algorithms for multiple change-point detection in multivariate variability based on data depth, with proven consistency and improved performance.

Findings

Methods outperform existing techniques in simulations.

Algorithms accurately detect change-points in heavy-tailed data.

Both methods are consistent for number and location of change-points.

Abstract

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.