Ditzhaus, MarcGaigall, Daniel2023-06-272023-06-272022-02-14http://hdl.handle.net/2003/4184310.17877/DE290R-23686This paper considers a paired data framework and discusses the question of marginal homogeneity of bivariate high-dimensional or functional data. The related testing problem can be endowed into a more general setting for paired random variables taking values in a general Hilbert space. To address this problem, a Cramér–von-Mises type test statistic is applied and a bootstrap procedure is suggested to obtain critical values and finally a consistent test. The desired properties of a bootstrap test can be derived that are asymptotic exactness under the null hypothesis and consistency under alternatives. Simulations show the quality of the test in the finite sample case. A possible application is the comparison of two possibly dependent stock market returns based on functional data. The approach is demonstrated based on historical data for different stock market indices.enTEST;31(3)https://creativecommons.org/licenses/by/4.0/Marginal homogeneityFunctional dataBootstrap testU-statisticCramér–von-Mises testStock market return310Article