IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v208y2025ics0047259x2500020x.html
   My bibliography  Save this article

Set-valued expectiles for ordered data analysis

Author

Listed:
  • Hamel, Andreas H.
  • Ha, Thi Khanh Linh

Abstract

Expectile regions–like depth regions in general–capture the idea of centrality of multivariate distributions. If an order relation is present for the values of random vectors and a decision maker is interested in dominant/best points with respect to this order, centrality is not a useful concept. Therefore, cone expectile sets are introduced which depend on a vector preorder generated by a convex cone. This provides a way of describing and clustering a multivariate distribution/data cloud with respect to an order relation. Fundamental properties of cone expectiles are established including dual representations of both expectile regions and cone expectile sets. It is shown that set-valued sublinear risk measures can be constructed from cone expectile sets in the same way as in the univariate case. Inverse functions of cone expectiles are defined which should be considered as ranking functions related to the initial order relation rather than as depth functions. Finally, expectile orders for random vectors are introduced and characterized via expectile ranking functions.

Suggested Citation

  • Hamel, Andreas H. & Ha, Thi Khanh Linh, 2025. "Set-valued expectiles for ordered data analysis," Journal of Multivariate Analysis, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:jmvana:v:208:y:2025:i:c:s0047259x2500020x
    DOI: 10.1016/j.jmva.2025.105425
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X2500020X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2025.105425?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.

    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:208:y:2025:i:c:s0047259x2500020x. 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.