TY  - JOUR
A1  - Ditzhaus, Marc
A1  - Gaigall, Daniel
T1  - Testing marginal homogeneity in Hilbert spaces with applications to stock market returns
JF  - Test
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.
Y1  - 2022
U6  - http://dx.doi.org/10.1007/s11749-022-00802-5
SN  - 1863-8260
VL  - 2022
IS  - 31
SP  - 749
EP  - 770
PB  - Springer
ER  - 
TY  - JOUR
A1  - Ditzhaus, Marc
A1  - Gaigall, Daniel
T1  - A consistent goodness-of-fit test for huge dimensional and functional data
JF  - Journal of Nonparametric Statistics
N2  - A nonparametric goodness-of-fit test for random variables with values in a separable Hilbert space is investigated. To verify the null hypothesis that the data come from a specific distribution, an integral type test based on a Cramér-von-Mises statistic is suggested. The convergence in distribution of the test statistic under the null hypothesis is proved and the test's consistency is concluded. Moreover, properties under local alternatives are discussed. Applications are given for data of huge but finite dimension and for functional data in infinite dimensional spaces. A general approach enables the treatment of incomplete data. In simulation studies the test competes with alternative proposals.
KW  - Cramér-von-Mises statistic
KW  - separable Hilbert space
KW  - huge dimensional data
KW  - functional data
Y1  - 2018
U6  - http://dx.doi.org/10.1080/10485252.2018.1486402
SN  - 1029-0311
VL  - 30
IS  - 4
SP  - 834
EP  - 859
PB  - Taylor & Francis
CY  - Abingdon
ER  -