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

Marc Ditzhaus () and Daniel Gaigall ()
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Marc Ditzhaus: TU Dortmund University
Daniel Gaigall: Leibniz University Hannover

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2022, vol. 31, issue 3, No 8, 749-770

Abstract: 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.

Keywords: Marginal homogeneity; Functional data; Bootstrap test; U-statistic; Cramér–von-Mises test; Stock market return; 62G10; 62G09 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11749-022-00802-5

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