Measuring and Testing Mutual Dependence of Multivariate Functional Data


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Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics, Statistics & Probability


ISSN: 1234-7655
eISSN: 2450-0291





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VOLUME 21 , ISSUE 3 (September 2020) > List of articles

Measuring and Testing Mutual Dependence of Multivariate Functional Data

Mirosław Krzyśko / Łukasz Smaga

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

Citation Information : Statistics in Transition New Series. Volume 21, Issue 3, Pages 21-37, DOI:

License : (CC BY-NC-ND 4.0)

Received Date : 17-December-2019 / Accepted: 11-May-2020 / Published Online: 20-September-2020



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.

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