Title: Nonparametric methods for change point analysis in multivariate, functional and network data
Authors: Shojaeddin Chenouri - University of Waterloo (Canada) [presenting]
Abstract: A nonparametric framework is introduced for change point analysis in variety of data settings such as multivariate, matrix valued, functional and network data. To motivate the methodology, we begin with multivariate case in which we propose a nonparametric change point test for multivariate data using rankings obtained from data depth measures. As the data depth of an observation measures its centrality relative to the sample, changes in data depth may signify a change of scale of the underlying distribution, and the proposed test is particularly responsive to detecting such changes. We provide a full asymptotic theory for the proposed test statistic under the null hypothesis that the observations are stable, and natural conditions under which the test is consistent. The finite sample properties are investigated by means of a Monte Carlo simulation, and these along with the theoretical results confirm that the test is robust to heavy tails, skewness, and high dimensionality. Finally, we extend the methodology to more general data structures by introducing appropriate depth measures.