IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v82y2012i10p1823-1828.html
   My bibliography  Save this article

How close are pairwise and mutual independence?

Author

Listed:
  • Nelsen, Roger B.
  • Úbeda-Flores, Manuel

Abstract

Using the technique of finding bounds on sets of copulas with particular properties, we compare the distribution of an n-dimensional (n≥3) vector of continuous pairwise independent random variables to the distribution of a similar vector of mutually independent random variables. We examine the n=3 case in detail, and provide asymptotic results in the general case.

Suggested Citation

  • Nelsen, Roger B. & Úbeda-Flores, Manuel, 2012. "How close are pairwise and mutual independence?," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1823-1828.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:10:p:1823-1828
    DOI: 10.1016/j.spl.2012.06.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212002179
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2012.06.006?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
    ---><---

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

    References listed on IDEAS

    as
    1. Alsina, Claudi & Nelsen, Roger B. & Schweizer, Berthold, 1993. "On the characterization of a class of binary operations on distribution functions," Statistics & Probability Letters, Elsevier, vol. 17(2), pages 85-89, May.
    2. Nelsen, Roger B. & Molina, José Juan Quesada & Lallena, José Antonio Rodríguez & Flores, Manuel Úbeda, 2004. "Best-possible bounds on sets of bivariate distribution functions," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 348-358, August.
    3. Fernández-Sánchez, Juan & Nelsen, Roger B. & Úbeda-Flores, Manuel, 2011. "Multivariate copulas, quasi-copulas and lattices," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1365-1369, September.
    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. repec:bpj:demode:v:6:y:2018:i:1:p:139-155:n:9 is not listed on IDEAS
    2. Fabrizio Durante & Erich Klement & Carlo Sempi & Manuel Úbeda-Flores, 2010. "Measures of non-exchangeability for bivariate random vectors," Statistical Papers, Springer, vol. 51(3), pages 687-699, September.
    3. Fabrizio Durante & Juan Fernández-Sánchez & Wolfgang Trutschnig & Manuel Úbeda-Flores, 2020. "On the Size of Subclasses of Quasi-Copulas and Their Dedekind–MacNeille Completion," Mathematics, MDPI, vol. 8(12), pages 1-11, December.
    4. Jonathan Ansari & Eva Lutkebohmert & Ariel Neufeld & Julian Sester, 2022. "Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information," Papers 2204.01071, arXiv.org, revised Sep 2023.
    5. Nelsen, Roger B. & Quesada-Molina, José Juan & Rodri­guez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2008. "On the construction of copulas and quasi-copulas with given diagonal sections," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 473-483, April.
    6. Azam Dehgani & Ali Dolati & Manuel Úbeda-Flores, 2013. "Measures of radial asymmetry for bivariate random vectors," Statistical Papers, Springer, vol. 54(2), pages 271-286, May.
    7. Kaas, Rob & Laeven, Roger J.A. & Nelsen, Roger B., 2009. "Worst VaR scenarios with given marginals and measures of association," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 146-158, April.
    8. Genest, C. & Quesada Molina, J. J. & Rodriguez Lallena, J. A. & Sempi, C., 1999. "A Characterization of Quasi-copulas," Journal of Multivariate Analysis, Elsevier, vol. 69(2), pages 193-205, May.
    9. Quesada Molina, Jose Juan & Sempi, Carlo, 2005. "Discrete quasi-copulas," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 27-41, August.
    10. Stefan Aulbach & Verena Bayer & Michael Falk, 2012. "A multivariate piecing-together approach with an application to operational loss data," Papers 1205.1617, arXiv.org.
    11. Butucea, Cristina & Delmas, Jean-François & Dutfoy, Anne & Fischer, Richard, 2015. "Maximum entropy copula with given diagonal section," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 61-81.
    12. Saminger-Platz Susanne & Klement Erich Peter & Arias-García José De Jesús & Mesiar Radko, 2017. "Characterizations of bivariate conic, extreme value, and Archimax copulas," Dependence Modeling, De Gruyter, vol. 5(1), pages 45-58, January.
    13. Yanqin Fan & Carlos A. Manzanares, 2017. "Partial identification of average treatment effects on the treated through difference-in-differences," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 1057-1080, October.
    14. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2011. "Aggregation functions: construction methods, conjunctive, disjunctive and mixed classes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00539032, HAL.
    15. Ali E. Abbas, 2009. "Multiattribute Utility Copulas," Operations Research, INFORMS, vol. 57(6), pages 1367-1383, December.
    16. Yanqin Fan & Sang Soo Park, 2009. "Partial identification of the distribution of treatment effects and its confidence sets," Advances in Econometrics, in: Nonparametric Econometric Methods, pages 3-70, Emerald Group Publishing Limited.
    17. B. Baets & H. Meyer & B. Schuymer, 2006. "Cyclic Evaluation of Transitivity of Reciprocal Relations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 217-238, April.
    18. Arnold, Sebastian & Molchanov, Ilya & Ziegel, Johanna F., 2020. "Bivariate distributions with ordered marginals," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    19. Murray D. Smith, 2005. "Using Copulas to Model Switching Regimes with an Application to Child Labour," The Economic Record, The Economic Society of Australia, vol. 81(s1), pages 47-57, August.
    20. Fernández-Sánchez, Juan & Nelsen, Roger B. & Úbeda-Flores, Manuel, 2011. "Multivariate copulas, quasi-copulas and lattices," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1365-1369, September.
    21. Durante Fabrizio & Puccetti Giovanni & Scherer Matthias & Vanduffel Steven, 2017. "My introduction to copulas: An interview with Roger Nelsen," Dependence Modeling, De Gruyter, vol. 5(1), pages 88-98, January.

    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:stapro:v:82:y:2012:i:10:p:1823-1828. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.