Graph-theoretic statistical methods for detecting and localizing distributional change in multivariate data

Abstract

This dissertation explores the topic of detecting and localizing change in a series of multivariate data using graph-theoretic statistical criteria. Change-detection methods based on graph theory are emerging due to their ability to detect change of a general nature with desirable power properties. The graph-theoretic structures of minimum non-bipartite matching and nearest neighbors according to distances between observations form the basis of our statistical procedures. We consider the computation time to implement the procedures with the detection power of the derived statistics. In a simulation study, we evaluate the power of our proposed statistical tests in a series of vignettes in which the sampling distribution, dimensionality, change parameter (location or scale), change type (abrupt or gradual), and change magnitude each are allowed to vary. We compare detection power with contemporary parametric and graph-theoretic approaches. Although our tests alone do not provide the information needed to localize a change point, we develop a follow-on procedure that satisfies this objective. We illustrate our proposed statistical tests and change-point localization techniques in an application, which demonstrates how several of the apparent limitations of our approach can be surmounted.