Application of the ρV coefficient and distance correlation to the analysis of multivariate association

Malwina Janiszewska; Anna Szczepańska-Álvarez; Emilia Zawieja

doi:10.2478/bile-2020-0009

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Application of the ρV coefficient and distance correlation to the analysis of multivariate association

Biometrical Letters

Volume 57 (2020): Issue 2 (December 2020)

By: Malwina Janiszewska, Anna Szczepańska-Álvarez and Emilia Zawieja

Open Access

|Dec 2020

Abstract

The aim of this paper is to study the association between two random vectors related to two groups of characteristics. To analyze the multivariate association, the ρV coefficient and distance correlation are used. Two methods (classical and recent) are compared and illustrated with real data.

References

Cléroux R., Lazraq A., Lepage Y.(1995): Vector correlation based on ranks and a nonparametric test of no association between vectors. Communications in Statistics Theory and Methods 24: 713–733.10.1080/03610929508831518
Search in Google Scholar Back to article
Escoufier Y. (1973): Le traitement des variables vectorielles. Biometrics 29: 751–760.10.2307/2529140
Search in Google Scholar Back to article
Gower J. (1966): Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 53: 325–338.10.1093/biomet/53.3-4.325
Search in Google Scholar Back to article
Heller R., Heller Y., Gorfine M. (2013): A consistent multivariate test of association based on ranks of distances. Biometrika 100: 503–510.10.1093/biomet/ass070
Search in Google Scholar Back to article
Husson F., Josse J., Le S., Mazet J. (2013): FactoMineR: Multivariate Exploratory Data Analysis and Data Mining with R. URL http://cran.r-project.org/package=FactoMineR, R package version 1.24.
Search in Google Scholar Back to article
Josse J., Pages J., Husson F. (2008): Testing the significance of rv coefficient. Computational Statistics and Data Analysis 53: 82–91.10.1016/j.csda.2008.06.012
Search in Google Scholar Back to article
Josse J., Holmes S. (2016): Measuring multivariate association and beyond. Statistics Surveys 10: 132–167.10.1214/16-SS116565814629081877
Search in Google Scholar Back to article
Tjøstheim D., Hufthammer K. (2013): Local Gaussian correlation: a new measure of dependence. Journal of Econometrics 172(1): 33–48.10.1016/j.jeconom.2012.08.001
Search in Google Scholar Back to article
Reshef D., Reshef Y., Finucane H., Grossman S., McVean G., Turnbaugh P., Lander E., Mitzenmacher M., Sabeti P.C. (2011): Detecting novel associations in large data sets. Science 334: 1518–1524.10.1126/science.1205438332579122174245
Search in Google Scholar Back to article
Székely G.J., Rizzo M.L., Bakirov N.K. (2007): Measuring and testing independence by correlation of distances. Annals of Statistics 35: 2769–2794.10.1214/009053607000000505
Search in Google Scholar Back to article
Székely G.J., Rizzo M.L., (2009): Brownian distance covariance. The Annals of Applied Statistics 3(4): 1236–1265.10.1214/09-AOAS312288950120574547
Search in Google Scholar Back to article
Székely G.J., Rizzo M.L. (2013): energy: E-statistics (energy statistics). URL http://CRAN.R-project.org/package=energy. R package version 1.6.0.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/bile-2020-0009 | Journal eISSN: 2199-577X | Journal ISSN: 1896-3811

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Language: English

Page range: 119 - 129

Published on: Dec 31, 2020

Published by: Polish Biometric Society

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

ρV coefficient,

distance correlation,

association between two random vectors

Related subjects:

Life sciences,

Bioinformatics,

Life sciences, other,

Mathematics,

Probability and statistics,

Applied mathematics

© 2020 Malwina Janiszewska, Anna Szczepańska-Álvarez, Emilia Zawieja, published by Polish Biometric Society
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 57 (2020): Issue 2 (December 2020)