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

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Authors
Hawks, Matthew A.
Subjects
Nonparametric test
non-bipartite matching
nearest neighbor
change point
Advisors
Koyak, Robert
Date of Issue
2015-06
Date
Jun-15
Publisher
Monterey, California: Naval Postgraduate School
Language
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.
Type
Thesis
Description
Series/Report No
Department
Applied Mathematics
Applied Mathematics
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Distribution Statement
Approved for public release; distribution is unlimited.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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