Two-sample Kolmogorov-Smirnov-type tests revisited: old and new tests in terms of local levels
To compare the distribution functions of two independent samples of independent observations, the two-sample Kolmogorov Smirnov test, comparing the distance of the empirical distribution function, is useful. Rewriting the test as an union-intersection test, the authors study the local level of the weighted Kolmogorov-Smirnov test, both for finite samples and asymptotically. The authors propose a two-sample test with approximately equal local levels. It is based on the minimum \(p\)-value principle. The authors also study the finite sample properties of this test. They compare the power to the power of the classical Kolmogorov-Smirnov test and the weighted Kolmogorov-Smirnov test. For normal random variables and the alternative of a change in variance, the new test has a good performance. Finally, a combination of the new test and the Kolmogorov-Smirnov test is proposed.
scientific article; zbMATH DE number 6968607
scientific article