IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v97y2006i3p765-784.html
   My bibliography  Save this article

Measuring stochastic dependence using [phi]-divergence

Author

Listed:
  • Micheas, Athanasios C.
  • Zografos, Konstantinos

Abstract

The problem of bivariate (multivariate) dependence has enjoyed the attention of researchers for over a century, since independence in the data is often a desired property. There exists a vast literature on measures of dependence, based mostly on the distance of the joint distribution of the data and the product of the marginal distributions, where the latter distribution assumes the property of independence. In this article, we explore measures of multivariate dependence based on the [phi]-divergence of the joint distribution of a random vector and the distribution that corresponds to independence of the components of the vector, the product of the marginals. Properties of these measures are also investigated and we employ and extend the axiomatic framework of Renyi [On measures of dependence, Acta Math. Acad. Sci. Hungar. 10 (1959) 441-451], in order to assert the importance of [phi]-divergence measures of dependence for a general convex function [phi] as well as special cases of [phi]. Moreover, we obtain point estimates as well as interval estimators when an elliptical distribution is used to model the data, based on [phi]-divergence via Monte Carlo methods.

Suggested Citation

  • Micheas, Athanasios C. & Zografos, Konstantinos, 2006. "Measuring stochastic dependence using [phi]-divergence," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 765-784, March.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:3:p:765-784
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(05)00051-5
    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. Ebrahimi, Nader & Jalali, Nima Y. & Soofi, Ehsan S., 2014. "Comparison, utility, and partition of dependence under absolutely continuous and singular distributions," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 32-50.
    2. Rodríguez, Jhan & Bárdossy, András, 2015. "Entropy measure for the quantification of upper quantile interdependence in multivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 317-324.
    3. Apratim Guha & Atanu Biswas & Abhik Ghosh, 2021. "A nonparametric two‐sample test using a general φ‐divergence‐based mutual information," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(2), pages 180-202, May.
    4. Karl Siburg & Pavel Stoimenov, 2010. "A measure of mutual complete dependence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(2), pages 239-251, March.
    5. Majid Asadi & Karthik Devarajan & Nader Ebrahimi & Ehsan Soofi & Lauren Spirko‐Burns, 2022. "Elaboration Models with Symmetric Information Divergence," International Statistical Review, International Statistical Institute, vol. 90(3), pages 499-524, December.

    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:97:y:2006:i:3:p:765-784. 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.

    We have no bibliographic 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.

    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.