197
Views
1
CrossRef citations to date
0
Altmetric
Research Article

Tests of mutual independence among several random vectors using univariate and multivariate ranks of nearest neighbours

ORCID Icon, ORCID Icon, ORCID Icon & ORCID Icon
Pages 1890-1906 | Received 15 Jun 2020, Accepted 11 Jan 2021, Published online: 04 Feb 2021

References

  • Anderson TW. An introduction to multivariate statistical analysis. New York: Wiley; 2003.
  • Puri ML, Sen PK. Nonparametric methods in multivariate analysis. New York: Wiley; 1971.
  • Taskinen S, Kankainen A, Oja H. Sign test of independence between two random vectors. Stat Prob Lett. 2003;62(1):9–21.
  • Taskinen S, Oja H, Randles RH. Multivariate nonparametric tests of independence. J Am Stat Assoc. 2005;100(471):916–925.
  • Gieser PW, Randles RH. A nonparametric test of independence between two vectors. J Am Stat Assoc. 1997;92(438):561–567.
  • Székely GJ, Rizzo ML, Bakirov NK. Measuring and testing dependence by correlation of distances. Ann Stat. 2007;35(6):2769–2794.
  • Gretton A, Fukumizu K, Teo CH, et al. A kernel statistical test of independence. In Advances in Neural Information Processing Systems. 2008. p. 585–592.
  • Heller R, Heller Y, Gorfine M. A consistent multivariate test of association based on ranks of distances. Biometrika. 2013;100(2):503–510.
  • Heller R, Gorfine M, Heller Y. A class of multivariate distribution-free tests of independence based on graphs. J Stat Plan Inference. 2012;142(12):3097–3106.
  • Biswas M, Sarkar S, Ghosh AK. On some exact distribution-free tests of independence between two random vectors of arbitrary dimensions. J Stat Plan Inference. 2016;175:78–86.
  • Sarkar S, Ghosh AK. Some multivariate tests of independence based on ranks of nearest neighbors. Technometrics. 2018;60(1):101–111.
  • Nelsen RB. Nonparametric measures of multivariate association. In Distributions with Fixed Marginals and Related Topics, Lecture Notes-Monograph Series. Vol. 28, 1996. p. 223–232.
  • Úbeda-Flores M. Multivariate versions of Blomqvist's beta and Spearman's footrule. Ann Inst Stat Math. 2005;57(4):781–788.
  • Gaißer S, Ruppert M, Schmid F. A multivariate version of Hoeffding's phi-square. J Multivar Anal. 2010;101(10):2571–2586.
  • Póczos B, Ghahramani Z, Schneider J. Copula-based kernel dependency measures. In Proceedings of the 29th International Conference on Machine Learning; New York: Omnipress; 2012. p. 775–782.
  • Roy A, Ghosh AK, Goswami A, et al. Some new copula based distribution-free tests of independence among several random variables. Sankhya, Ser A. 2020. doi: https://doi.org/10.1007/s13171-020-00207-2.
  • Bilodeau M, Lafaye de Micheaux P. A multivariate empirical characteristic function test of independence with normal marginals. J Multivar Anal. 2005;95(2):345–369.
  • Beran R, Bilodeau M, Lafaye de Micheaux P. Nonparametric tests of independence between random vectors. J Multivar Anal. 2007;98(9):1805–1824.
  • Matteson DS, Tsay RS. Independent component analysis via distance covariance. J Am Stat Assoc. 2017;112(518):623–637.
  • Fan Y, Lafaye de Micheaux P, Penev S, et al. Multivariate nonparametric test of independence. J Multivar Anal. 2017;153:189–210.
  • Chakraborty S, Zhang X. Distance metrics for measuring joint dependence with application to causal inference. J Am Stat Assoc. 2019;114(528):1638–1650.
  • Bilodeau M, Nangue AG. Tests of mutual or serial independence of random vectors with applications. J Mach Learn Res. 2017;18(74):1–40.
  • Pfister N, Bühlmann P, Schölkopf B, et al. Kernel-based tests for joint independence. J R Stat Soc Ser B. 2018;80(1):5–31.
  • Friedman JH, Rafsky LC. Graph-theoretic measures of multivariate association and prediction. Ann Stat. 1983;11(2):377–391.
  • Jin Z, Matteson DS. Generalizing distance covariance to measure and test multivariate mutual dependence via complete and incomplete v-statistics. J Multivar Anal. 2018;168:304–322.
  • Witmer J. Data analysis: an introduction. New Jersey: Prentice Hall; 1997.
  • Hochberg Y. A sharper Bonferroni procedure for multiple tests of significance. Biometrika. 1988;75(4):800–802.
  • Peters J, Mooij JM, Janzing D, et al. Causal discovery with continuous additive noise models. J Mach Learn Res. 2014;15(58):2009–2053.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.