IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v46y2000i4p371-379.html
   My bibliography  Save this article

Link between grade measures of dependence and of separability in pairs of conditional distributions

Author

Listed:
  • Kowalczyk, Teresa

Abstract

Two grade measures of monotone dependence, Spearman's [rho]* and Kendall's [tau], can be expressed as weighted averages of monotone Gini separation indices for pairs of conditional distributions of Y on X. This fact is used to show an important property of the measures of absolute dependence [rho]max* and [tau]max, defined, respectively, as the maximal values of [rho]* and [tau] over the set of pairs of all the possible one-to-one Borel-measurable transformations of X and of Y. Namely, if (X,Y) are totally positive of order two (TP2) then [rho]*(X,Y)=[rho]max*(X,Y) and [tau](X,Y)=[tau]max(X,Y). Moreover, another index [tau]abs(X,Y) of absolute dependence is introduced as weighted average of Gini (absolute) separation indices for the pairs of conditional distributions of Y on X. Indices [tau]abs and [tau]max are used to measure the irregularity of dependence. All facts proved in this paper hold for the general case of the mixed discrete-continuous variables.

Suggested Citation

  • Kowalczyk, Teresa, 2000. "Link between grade measures of dependence and of separability in pairs of conditional distributions," Statistics & Probability Letters, Elsevier, vol. 46(4), pages 371-379, February.
    • Handle: RePEc:eee:stapro:v:46:y:2000:i:4:p:371-379
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(99)00125-X
    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.

    References listed on IDEAS

    as
    1. Wieslaw Szczesny, 1991. "On the performance of a discriminant function," Journal of Classification, Springer;The Classification Society, vol. 8(2), pages 201-215, December.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Monika Piwowar & Kinga A Kocemba-Pilarczyk & Piotr Piwowar, 2018. "Regularization and grouping -omics data by GCA method: A transcriptomic case," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-14, November.
    2. Kowalczyk, T. & Niewiadomska-Bugaj, M., 2000. "Decomposition of Kendall's [tau]: implications for clustering," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 375-383, July.
    3. Kowalczyk, T. & Niewiadomska-Bugaj, M., 2001. "An algorithm for maximizing Kendall's [tau]," Computational Statistics & Data Analysis, Elsevier, vol. 37(2), pages 181-193, August.

    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. Monika Piwowar & Kinga A Kocemba-Pilarczyk & Piotr Piwowar, 2018. "Regularization and grouping -omics data by GCA method: A transcriptomic case," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-14, November.
    2. Krzysztof Gajowniczek & Tomasz Ząbkowski, 2017. "Electricity forecasting on the individual household level enhanced based on activity patterns," PLOS ONE, Public Library of Science, vol. 12(4), pages 1-26, April.
    3. Krzysztof Gajowniczek & Tomasz Ząbkowski, 2015. "Data Mining Techniques for Detecting Household Characteristics Based on Smart Meter Data," Energies, MDPI, vol. 8(7), pages 1-21, July.
    4. Ciok, Alicja, 1996. "An estimator of Gini Separation Index which is nearly median-unbiased," Computational Statistics & Data Analysis, Elsevier, vol. 21(5), pages 533-546, May.

    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:46:y:2000:i:4:p:371-379. 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.