@article{DitzhausGaigall2022,
  author    = {Ditzhaus, Marc and Gaigall, Daniel},
  title     = {Testing marginal homogeneity in Hilbert spaces with applications to stock market returns},
  series = {Test},
  volume    = {2022},
  journal   = {Test},
  number    = {31},
  publisher = {Springer},
  issn      = {1863-8260},
  doi       = {10.1007/s11749-022-00802-5},
  pages     = {749 -- 770},
  year      = {2022},
  abstract  = {This 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 Cram{\´e}r-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.},
  language  = {en}
}