Measuring and Testing Mutual Dependence of Multivariate Functional Data

Mirosław Krzyśko; Łukasz Smaga

doi:DOI 10.21307/stattrans-2020-042

Measuring and Testing Mutual Dependence of Multivariate Functional Data

Mirosław Krzyśko Interfaculty Institute of Mathematics and Statistics, The President Stanisław Wojciechowski State University of Applied Sciences in Kalisz, Poland ORCID:https://orcid.org/0000-0001- 8075-4432 , Łukasz Smaga Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland ORCID:https://orcid.org/0000-0002-2442-8816 Statistics in Transition new series, vol. 21, 2020, 3, pages: 21-37 Published online: 4 September 2020 DOI DOI 10.21307/stattrans-2020-042

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ABSTRACT

This paper considers new measures of mutual dependence between multiple multivariate random processes representing multidimensional functional data. In the case of two processes, the extension of functional distance correlation is used by selecting appropriate weight function in the weighted distance between characteristic functions of joint and marginal distributions. For multiple random processes, two measures are sums of squared measures for pairwise dependence. The dependence measures are zero if and only if the random processes are mutually independent. This property is used to construct permutation tests for mutual independence of random processes. The finite sample properties of these tests are investigated in simulation studies. The use of the tests and the results of simulation studies are illustrated with an example based on real data.

KEYWORDS

characteristic function, dependence measure, distance covariance, multivariate functional data, permutation method, test of independence

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