Testing marginal homogeneity in Hilbert spaces with applications to stock market returns
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Marc Ditzhaus [1] ; Daniel Gaigall [2]
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[1] Technical University of Dortmund
Technical University of Dortmund
Kreisfreie Stadt Dortmund, Alemania
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[2] Institute of Actuarial and Financial Mathematics, Leibniz University Hannover
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- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 31, Nº. 3, 2022, págs. 749-770
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
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.
