IDEAS home Printed from
   My bibliography  Save this article

Integral trimmed regions


  • Cascos, Ignacio
  • López-Díaz, Miguel


We define a new family of central regions with respect to a probability measure. They are induced by a set or a family of sets of functions and we name them integral trimmed regions. The halfspace trimming and the zonoid trimming are particular cases of integral trimmed regions. We focus our work on the derivation of properties of such integral trimmed regions from conditions satisfied by the generating classes of functions. Further we show that, under mild conditions, the population integral trimmed region of a given depth can be characterized in terms of certain regions based on empirical distributions.

Suggested Citation

  • Cascos, Ignacio & López-Díaz, Miguel, 2005. "Integral trimmed regions," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 404-424, October.
  • Handle: RePEc:eee:jmvana:v:96:y:2005:i:2:p:404-424

    Download full text from publisher

    File URL:
    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

    1. Fernández, Ignacio Cascos & Molchanov, Ilya, 2003. "A stochastic order for random vectors and random sets based on the Aumann expectation," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 295-305, July.
    2. Masse, J. C. & Theodorescu, R., 1994. "Halfplane Trimming for Bivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 48(2), pages 188-202, February.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Cascos, Ignacio & López-Díaz, Miguel, 2012. "Trimmed regions induced by parameters of a probability," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 306-318.
    2. Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008. "Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth," Working Papers ECARES 2008_042, ULB -- Universite Libre de Bruxelles.
    3. Ignacio Cascos & Ilya Molchanov, 2006. "Multivariate risks and depth-trimmed regions," Papers math/0606520,, revised Nov 2006.
    4. Cascos, Ignacio, 2006. "The expected convex hull trimmed regions of a sample," DES - Working Papers. Statistics and Econometrics. WS ws066919, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Cascos, Ignacio & Molchanov, Ilya, 2006. "Multivariate risks and depth-trimmed regions," DES - Working Papers. Statistics and Econometrics. WS ws063815, Universidad Carlos III de Madrid. Departamento de Estadística.


    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:96:y:2005:i:2:p:404-424. 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: .

    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 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.

    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.