IDEAS home Printed from https://ideas.repec.org/a/vrs/stintr/v21y2020i3p21-37n9.html
   My bibliography  Save this article

Measuring and Testing Mutual Dependence of Multivariate Functional Data

Author

Listed:
  • 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, Statistics Poland, 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.21307/stattrans-2020-042
    Download Restriction: no
    File URL: https://libkey.io/10.21307/stattrans-2020-042?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. John Nolan, 2013. "Multivariate elliptically contoured stable distributions: theory and estimation," Computational Statistics, Springer, vol. 28(5), pages 2067-2089, October.
    3. 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.
    4. Horváth, Lajos & Rice, Gregory, 2015. "Testing for independence between functional time series," Journal of Econometrics, Elsevier, vol. 189(2), pages 371-382.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mirosław Krzyśko & Łukasz Smaga, 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.
    2. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2021. "Testing serial independence with functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 603-629, September.
    3. Meintanis, Simos G. & Hušková, Marie & Hlávka, Zdeněk, 2022. "Fourier-type tests of mutual independence between functional time series," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    4. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2020. "Change-point methods for multivariate time-series: paired vectorial observations," Statistical Papers, Springer, vol. 61(4), pages 1351-1383, August.
    5. Hušková, Marie & Meintanis, Simos G. & Pretorius, Charl, 2020. "Tests for validity of the semiparametric heteroskedastic transformation model," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    6. Chen, Feifei & Jiménez–Gamero, M. Dolores & Meintanis, Simos & Zhu, Lixing, 2022. "A general Monte Carlo method for multivariate goodness–of–fit testing applied to elliptical families," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    7. Norbert Henze & Pierre Lafaye De Micheaux & Simos G. Meintanis, 2022. "Tests for circular symmetry of complex-valued random vectors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 488-518, June.
    8. Vexler, Albert & Zou, Li, 2022. "Linear projections of joint symmetry and independence applied to exact testing treatment effects based on multidimensional outcomes," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    9. Sang, Yongli, 2024. "Test for diagonal symmetry in high dimension," Statistics & Probability Letters, Elsevier, vol. 205(C).
    10. Fraiman, Ricardo & Moreno, Leonardo & Ransford, Thomas, 2023. "A Cramér–Wold theorem for elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    11. Ling, S. & McAleer, M.J. & Tong, H., 2015. "Frontiers in Time Series and Financial Econometrics," Econometric Institute Research Papers EI 2015-07, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Quessy, Jean-François, 2021. "A Szekely–Rizzo inequality for testing general copula homogeneity hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    13. Lorenzo Ricci & David Veredas, 2012. "TailCoR," Working Papers 1227, Banco de España.
      • Sla{dj}ana Babi'c & Christophe Ley & Lorenzo Ricci & David Veredas, 2020. "TailCoR," Papers 2011.14817, arXiv.org.
    14. Berkes, István & Horváth, Lajos & Rice, Gregory, 2016. "On the asymptotic normality of kernel estimators of the long run covariance of functional time series," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 150-175.
    15. Ling, Shiqing & McAleer, Michael & Tong, Howell, 2015. "Frontiers in Time Series and Financial Econometrics: An overview," Journal of Econometrics, Elsevier, vol. 189(2), pages 245-250.
    16. Christian Gourieroux & Joann Jasiak, 2023. "Generalized Covariance Estimator," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1315-1327, October.
    17. John P. Nolan, 2016. "An R package for modeling and simulating generalized spherical and related distributions," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-11, December.
    18. Denis Belomestny & Leonid Iosipoi, 2019. "Fourier transform MCMC, heavy tailed distributions and geometric ergodicity," Papers 1909.00698, arXiv.org, revised Dec 2019.
    19. Niels Wesselhöfft & Wolfgang K. Härdle, 2020. "Risk-Constrained Kelly Portfolios Under Alpha-Stable Laws," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 801-826, March.
    20. Belomestny, Denis & Iosipoi, Leonid, 2021. "Fourier transform MCMC, heavy-tailed distributions, and geometric ergodicity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 351-363.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:vrs:stintr:v:21:y:2020:i:3:p:21-37:n:9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://stat.gov.pl/en/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.