  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.
