Ball divergence: nonparametric two sample test
The authors introduce a novel measure between two probability measures called the ball divergence. It relies on the well-known fact that two probability measures on a separable Banach space equal if and only if they coincide on all balls. By constructing a finite sample version of the ball divergence, a nonparametric two sample test is constructed, which allows to test the null hypothesis that both measures are equal. This testing procedure can be interpreted as some sort of rank test, but differs fundamentally from the classic Kolmogorov-Smirnov and the Cramér-von Mises test. Letting the sizes \(n\) and \(m\) of the two samples tend to \(\infty\), the authors provide asymptotic distributions of the test statistic under the null hypothesis and the alternative hypothesis that the underlying measures are different. Finally it is shown that the test based on the finite sample ball divergence is consistent against any general alternative, no matter what the ratio of \(n\) and \(m\) is. Besides working without any moment assumption, this implies that the test can also cope with imbalanced data. Finally, finite sample properties of the test are investigated in a simulation study and on two real data examples from virtual drug screening and hormone replacement therapy.
scientific article; zbMATH DE number 6897924
scientific article