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Abstract:
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Of the several multivariate two-sample tests of equality, those based on graphs such as the minimum spanning tree, nearest neighbor, or optimal matching have shown considerable promise. We present a generalized multisample test of equality which uses the number of edges in a graph that connect observations from di?erent samples. We derive the mean, variance, and asymptotic distribution of this test statistic conditioned on the topology of the graph. We ?nd the power of this statistic for various graphs is larger than that of the energy statistic when samples di?er in location and scale simultaneously, which is usually the more interesting alternative. Finally, we apply these graph-theoretic tests to the problem of detecting a distributional change in multivariate data streams and ?nd they are typically superior to a technique using density estimation.
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