Cramér–von Mises and characteristic function tests for the two and kk-sample problems with dependent data

Statistical procedures for the equality of two and kk univariate distributions based on samples of dependent observations are proposed in this work. The test statistics are L2L2 distances of standard empirical and characteristic function processes. The pp-values of the tests are obtained from a version of the multiplier central limit theorem whose asymptotic validity is established. Simple formulas for the test statistics and their multiplier versions in terms of multiplication of matrices are provided. Simulations under many patterns of dependence characterized by copulas show the good behavior of the tests in small samples, both in terms of their power and of their ability to keep their nominal level under the null hypothesis.