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Testing marginal homogeneity in Hilbert spaces with applications to stock market returns

Author

Listed:
  • Marc Ditzhaus

    (TU Dortmund University)

  • Daniel Gaigall

    (Leibniz University Hannover)

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 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.

Suggested Citation

  • Marc Ditzhaus & Daniel Gaigall, 2022. "Testing marginal homogeneity in Hilbert spaces with applications to stock market returns," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 749-770, September.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:3:d:10.1007_s11749-022-00802-5
    DOI: 10.1007/s11749-022-00802-5
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    References listed on IDEAS

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