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<p>We propose new nonparametric statistical tests to identify whether each element in a sequence of independent multivariate  observations is drawn from a common probability distribution or if some distributional change has occurred over the course of  the sequence. Each test is formulated using matching techniques based on distances between observations. These tests are  capable of detecting changes of quite general nature, and, unlike most similar tests, they require no distribution assumptions or  any prior separation of the data into hypothetical pre- and post-change subsets. We derive a central limit theorem for one of the  tests and an exact distribution for another. A third culminating test, which is a cumulative sum of statistics on a collection of  orthogonal matchings associated with the observation sequence, exhibits noteworthy power to detect whether a distributional  change has occurred. We examine the performance of the tests by computer simulation and compare results to a state-of-the-art  parametric competitor.
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<br>Subjects: Nonparametric test; distribution-free test; non-bipartite matching; bipartite matching; change point</div>
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Ruth, David M.</div>
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