TY - JOUR

T1 - Testing marginal homogeneity in Hilbert spaces with applications to stock market returns

AU - Ditzhaus, Marc

AU - Gaigall, Daniel

N1 - Funding Information: The authors are grateful to the editor, the associate editor, and the two referees for their comments that substantially improved the paper’s quality. Moreover, the authors gratefully acknowledge the computing time provided on the Linux HPC cluster at TU Dortmund (LiDO3), partially funded by the Deutsche Forschungsgemeinschaft as project 271512359.

PY - 2022/9

Y1 - 2022/9

N2 - 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.

AB - 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.

KW - Bootstrap test

KW - Cramér–von-Mises test

KW - Functional data

KW - Marginal homogeneity

KW - Stock market return

KW - U-statistic

UR - http://www.scopus.com/inward/record.url?scp=85124741090&partnerID=8YFLogxK

U2 - 10.1007/s11749-022-00802-5

DO - 10.1007/s11749-022-00802-5

M3 - Article

VL - 31

SP - 749

EP - 770

JO - TEST

JF - TEST

IS - 3

ER -