Abstract
A new test for equal distributions of several high-dimensional samples in separable metric spaces, with its test statistic constructed based on maximum mean discrepancy, is proposed and studied. The asymptotic null and alternative distributions of the test statistic are established under some mild conditions. The new test is implemented via a three-cumulant matched chi-square approximation with the associated approximation parameters consistently estimated from the data. A new data-adaptive Gaussian kernel width selection method is also suggested. Good performance of the new test is illustrated by intensive simulation studies and a real data example of Gini index curves.
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