BazEkon - The Main Library of the Cracow University of Economics

BazEkon home page

Main menu

Author
Krzyśko Mirosław (The President Stanisław Wojciechowski State University of Applied Sciences in Kalisz, Poland), Smaga Łukasz (Adam Mickiewicz University in Poznań, Poland)
Title
Measuring and Testing Mutual Dependence of Multivariate Functional Data
Source
Statistics in Transition, 2020, vol. 21, nr 3, s. 21-37, rys., tab., bibliogr. s. 35-37
Keyword
Analiza zależności, Analiza danych funkcjonalnych, Miara odległości, Wielowymiarowa analiza statystyczna
Dependency analysis, Functional data analysis, Distance measures, Multi-dimensional statistical analysis
Note
summ.
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. (original abstract)
Accessibility
The Main Library of the Cracow University of Economics
The Library of Warsaw School of Economics
The Library of University of Economics in Katowice
Full text
Show
Bibliography
Show
  1. BOSQ, D., (2000). Linear Processes in Function Spaces. Theory and Applications, Springer.
  2. CHEN, F., MEINTANIS, S. G., ZHU, L., (2019). On some Characterizations and Multidimensional Criteria for Testing Homogeneity, Symmetry and Independence. Journal of Multivariate Analysis, 173, pp. 125-144.
  3. CUEVAS, A., (2014). A Partial Overview of the Theory of Statistics with Functional Data. Journal of Statistical Planning and Inference, 147, pp. 1-23.
  4. ESCOUFIER, Y., (1970). Echantillonnage dans une population de variables aléatoires réelles. Ph.D thesis, Université des Sciences et Techniques du Languedoc, Montpellier.
  5. ESCOUFIER, Y., (1973). Le Traitement des Variables Vectorielles. Biometrics, 29, pp. 751-760.
  6. FERRATY, F., VIEU, P., (2006). Nonparametric Functional Data Analysis: Theory and Practice, Springer: New York.
  7. GÓRECKI, T., KRZYŚKO, M., RATAJCZAK, W., WOŁYŃSKI, W., (2016). An Extension of the Classical Distance Correlation Coefficient for Multivariate Functional Data with Applications. Statistics in Transition new series, 17, pp. 449-466.
  8. GÓRECKI, T., KRZYSKO, M., WOŁYŃSKI, W., (2017). Correlation Analysis for Multivariate Functional Data. Studies in Classification, Data Analysis, and Knowledge Organization: Data Science, pp. 243-258.
  9. GÓRECKI, T., KRZYSKO, M., WOŁYŃSKI, W., (2019). Variable Selection in Multivariate Functional Data Classification. Statistics in Transition new series, 20, pp. 123-138.
  10. HE, G., MÜLLER, H. G., WANG, J. L., (2004). Methods of Canonical Analysis for Functional Data. Journal of Statistical Planning and Inference, 122, pp. 141-159.
  11. HLÁVKA, Z., HUŠKOVÁ, M., MEINTANIS, S. G., (2020). Change-Point Methods for Multivariate Time-Series: Paired Vectorial Observations. Statistical Papers, DOI: https://doi.org/10.1007/s00362-020-01175-3.
  12. HORVÁTH, L., KOKOSZKA, P., (2012). Inference for Functional Data with Applications, Springer.
  13. HORVÁTH, L., RICE, G., (2015). Testing for Independence between Functional Time Series. Journal of Econometrics, 189, pp. 371-382.
  14. HOTELLING, H., (1936). Relation Between Two Sets of Variables. Biometrika, 28, pp. 321-377.
  15. JIN, Z., MATTESON, D. S., (2018). Generalizing Distance Covariance to Measure and Test Multivariate Mutual Dependence via Complete and Incomplete V-statistics. Journal of Multivariate Analysis, 168, pp. 304-322.
  16. KOKOSZKA, P., REIMHERR, M., (2017). Introduction to Functional Data Analysis. Chapman and Hall/CRC.
  17. KRZYŚKO, M., SMAGA, Ł., (2019). Robust Estimation in Canonical Correlation Analysis for Multivariate Functional Data. Hacettepe Journal of Mathematics and Statistics, 48, pp. 521-535.
  18. KRZYŚKO, M., WASZAK, Ł., (2013). Canonical Correlation Analysis for Functional Data. Biometrical Letters, 50, pp. 95-105.
  19. LEURGANS, S. E., MOYEED, R. A., SILVERMAN, B. W., (1993). Canonical Correlation Analysis when the Data are Curves. Journal of the Royal Statistical Society. Series B (Methodological), 55, pp. 725-740.
  20. NOLAN, J. P., (2013). Multivariate Elliptically Contoured Stable Distributions: Theory and Estimation. Computational Statistics, 28, pp. 2067-2089.
  21. R CORE TEAM (2019). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.
  22. RAMSAY, J. O., SILVERMAN, B. W. (2005). Functional Data Analysis, Second Edition, Springer.
  23. RAMSAY, J. O., WICKHAM, H., GRAVES, S., HOOKER, G., (2018). fda: Functional Data Analysis. R package version 2.4.8. https://CRAN.R-project.org/ package=fda
  24. RIZZO, M. L., SZÉKELY, G. J., (2019). energy: E-Statistics: Multivariate Inference via the Energy of Data. R package version 1.7-6. https://CRAN.R-project.org/package=energy
  25. SZÉKELY, G. J., RIZZO, M. L., BAKIROV, N. K., (2007). Measuring and Testing Dependence by Correlation of Distances. The Annals of Statistics, 35, pp. 2769-2794.
  26. WANG, J. L., CHIOU, J. M., Müller, H. G., (2016). Functional Data Analysis. Annual Review of Statistics and Its Application, 3, pp. 257-295.
  27. ZHANG, J. T., (2013). Analysis of Variance for Functional Data. Chapman & Hall: London.
  28. ZOLOTAREV, V. M., (1981). Integral Transformations of Distributions and Estimates of Parameters of Multidimensional Spherically Symmetric Stable Laws. In Contributions to Probability: A Collection of Papers Dedicated to Eugene Lukacs, Academic Press, New York-London, pp. 283-305.
Cited by
Show
ISSN
1234-7655
Language
eng
URI / DOI
http://dx.doi.org/10.21307/stattrans-2020-042
Share on Facebook Share on Twitter Share on Google+ Share on Pinterest Share on LinkedIn Wyślij znajomemu