IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v11y1981i1p102-113.html
   My bibliography  Save this article

An asymptotic decomposition for multivariate distribution-free tests of independence

Author

Listed:
  • Deheuvels, Paul

Abstract

In the multivariate case, the empirical dependence function, defined as the empirical distribution function with reduced uniform margins on the unit interval, can be shown for an i.i.d. sequence to converge weakly in an asymptotic way to a limiting Gaussian process. The main result of this paper is that this limiting process can be canonically separated into a finite set of independent Gaussian processes, enabling one to test the existence of dependence relationships within each subset of coordinates independently (in an asymptotic way) of what occurs in the other subsets. As an application we derive the Karhunen-Loeve expansions of the corresponding processes and give the limiting distribution of the multivariate Cramer-Von Mises test of independence, generalizing results of Blum, Kiefer, Rosenblatt, and Dugué. Other extensions are mentioned, including a generalization of Kendall's [tau].

Suggested Citation

  • Deheuvels, Paul, 1981. "An asymptotic decomposition for multivariate distribution-free tests of independence," Journal of Multivariate Analysis, Elsevier, vol. 11(1), pages 102-113, March.
  • Handle: RePEc:eee:jmvana:v:11:y:1981:i:1:p:102-113
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(81)90136-6
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gautier Marti & Philippe Very & Philippe Donnat, 2015. "Toward a generic representation of random variables for machine learning," Working Papers hal-01196883, HAL.
    2. Einmahl, J.H.J. & McKeague, I.W., 2002. "Empirical Likelihood based on Hypothesis Testing," Discussion Paper 2002-92, Tilburg University, Center for Economic Research.
    3. Bilodeau, M. & Lafaye de Micheaux, P., 2005. "A multivariate empirical characteristic function test of independence with normal marginals," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 345-369, August.
    4. Rémillard, Bruno & Scaillet, Olivier, 2009. "Testing for equality between two copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 377-386, March.
    5. Bakirov, Nail K. & Rizzo, Maria L. & Szekely, Gábor J., 2006. "A multivariate nonparametric test of independence," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1742-1756, September.
    6. repec:eee:jmvana:v:166:y:2018:i:c:p:266-281 is not listed on IDEAS
    7. Genest, Christian & Quessy, Jean-François & Rémillard, Bruno, 2006. "Local efficiency of a Cramer-von Mises test of independence," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 274-294, January.
    8. Genest, Christian & Nešlehová, Johanna G. & Rémillard, Bruno, 2013. "On the estimation of Spearman’s rho and related tests of independence for possibly discontinuous multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 214-228.
    9. Gautier Marti & Frank Nielsen & Philippe Donnat & S'ebastien Andler, 2016. "On clustering financial time series: a need for distances between dependent random variables," Papers 1603.07822, arXiv.org.
    10. McKeague, Ian W. & Sun, Yanqing, 1996. "Transformations of Gaussian random fields to Brownian sheet and nonparametric change-point tests," Statistics & Probability Letters, Elsevier, vol. 28(4), pages 311-319, August.
    11. Koning, Alex J. & Protasov, Vladimir, 2003. "Tail behaviour of Gaussian processes with applications to the Brownian pillow," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 370-397, November.
    12. Pycke, Jean-Renaud, 2003. "Multivariate extensions of the Anderson-Darling process," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 387-399, July.
    13. Christian Genest & Bruno Rémillard, 2004. "Test of independence and randomness based on the empirical copula process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 335-369, December.
    14. García, Jesús E. & González-López, V.A. & Nelsen, R.B., 2013. "A new index to measure positive dependence in trivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 481-495.
    15. Beran, R. & Bilodeau, M. & Lafaye de Micheaux, P., 2007. "Nonparametric tests of independence between random vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1805-1824, October.
    16. Koning, A.J. & Protassov, V., 2001. "Tail behaviour of Gaussian processes with applications to the Brownian pillow," Econometric Institute Research Papers EI 2001-49, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    17. Kojadinovic, Ivan & Holmes, Mark, 2009. "Tests of independence among continuous random vectors based on Cramr-von Mises functionals of the empirical copula process," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1137-1154, July.

    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:eee:jmvana:v:11:y:1981:i:1:p:102-113. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.