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In this paper, we introduce two robust, nonparametric methods for multiplechange-point detection in the variability of a multivariate sequence ofobservations. We demonstrate that changes in ranks generated from data depthfunctions can be used to detect changes in the variability of a sequence ofmultivariate observations. In order to detect more than one change, the firstalgorithm uses methods similar to that of wild-binary segmentation. The secondalgorithm estimates change-points by maximizing a penalized version of theclassical Kruskal Wallis ANOVA test statistic. We show that this objectivefunction can be maximized via the well-known PELT algorithm. Under mild,nonparametric assumptions both of these algorithms are shown to be consistentfor the correct number of change-points and the correct location(s) of thechange-point(s). We demonstrate the efficacy of these methods with a simulationstudy, where we compare our new methods to several competing methods. We showour methods outperform existing methods in this problem setting, and ourmethods can estimate changes accurately when the data are heavy tailed orskewed.

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