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Measuring and Testing Mutual Dependence of Multivariate Functional Data

Author

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  • Krzyśko Mirosław

    (Interfaculty Institute of Mathematics and Statistics, The President Stanisław Wojciechowski State University of Applied Sciences, in Kalisz, Poland .)

  • Smaga Łukasz

    (Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland .)

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.

Suggested Citation

  • Krzyśko Mirosław & Smaga Łukasz, 2020. "Measuring and Testing Mutual Dependence of Multivariate Functional Data," Statistics in Transition New Series, Polish Statistical Association, vol. 21(3), pages 21-37, September.
    • Handle: RePEc:vrs:stintr:v:21:y:2020:i:3:p:21-37:n:9
    DOI: 10.21307/stattrans-2020-042
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    References listed on IDEAS

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    1. Chen, Feifei & Meintanis, Simos G. & Zhu, Lixing, 2019. "On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 125-144.
    2. Jin, Ze & Matteson, David S., 2018. "Generalizing distance covariance to measure and test multivariate mutual dependence via complete and incomplete V-statistics," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 304-322.
    3. Horváth, Lajos & Rice, Gregory, 2015. "Testing for independence between functional time series," Journal of Econometrics, Elsevier, vol. 189(2), pages 371-382.
    4. John Nolan, 2013. "Multivariate elliptically contoured stable distributions: theory and estimation," Computational Statistics, Springer, vol. 28(5), pages 2067-2089, October.
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