A0969
Title: Changepoint detection in the variability of multivariate and functional data
Authors: Kelly Ramsay - York University (Canada) [presenting]
Shojaeddin Chenouri - University of Waterloo (Canada)
Abstract: The problem of robustly detecting changepoints is considered in the variability of a sequence of independent multivariate functions and vectors. Novel changepoint procedures, called the functional and multivariate Kruskal-Wallis for covariance (FKWC and MKWC) changepoint procedures, are presented based on rank statistics and data depth. The MKWC and FKWC changepoint procedures allow the user to test for at most one changepoint or an epidemic period or to estimate the number and locations of an unknown amount of changepoints in the data. It is shown that when the "signal-to-noise'' ratio is bounded below, the changepoint estimates produced by the MKWC and FKWC procedures attain the minimax localization rate for detecting general changes in distribution in the univariate setting. The behavior of the proposed test statistics is also provided for the AMOC and epidemic setting under the null hypothesis, and, as a simple consequence of the main result, these tests are consistent.
