Applications of assignment algorithms to nonparametric tests for homogeneity
Ruth, David M.
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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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