IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/125584.html
   My bibliography  Save this paper

A simple measure of conditional dependence

Author

Listed:
  • Azadkia, Mona
  • Chatterjee, Sourav

Abstract

We propose a coefficient of conditional dependence between two random variables Y and Z given a set of other variables X1, . . . , Xp, based on an i.i.d. sample. The coefficient has a long list of desirable properties, the most important of which is that under absolutely no distributional assumptions, it converges to a limit in [0, 1], where the limit is 0 if and only if Y and Z are conditionally independent given X1, . . . , Xp, and is 1 if and only if Y is equal to a measurable function of Z given X1, . . . , Xp. Moreover, it has a natural interpretation as a nonlinear generalization of the familiar partial R2 statistic for measuring conditional dependence by regression. Using this statistic, we devise a new variable selection algorithm, called Feature Ordering by Conditional Independence (FOCI), which is model-free, has no tuning parameters, and is provably consistent under sparsity assumptions. A number of applications to synthetic and real datasets are worked out.

Suggested Citation

  • Azadkia, Mona & Chatterjee, Sourav, 2021. "A simple measure of conditional dependence," LSE Research Online Documents on Economics 125584, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:125584
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/125584/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Ansari Jonathan & Rockel Marcus, 2024. "Dependence properties of bivariate copula families," Dependence Modeling, De Gruyter, vol. 12(1), pages 1-36.

    More about this item

    Keywords

    conditional dependence; non-parametric measures of association; variable selection;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    Statistics

    Access and download statistics

    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:ehl:lserod:125584. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    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.