IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-031-61853-6_10.html
   My bibliography  Save this book chapter

An Asymptotic Expansion of the Empirical Angular Measure for Bivariate Extremal Dependence

In: Recent Advances in Econometrics and Statistics

Author

Listed:
  • Stéphane Lhaut

    (UCLouvain, LIDAM/ISBA)

  • Johan Segers

    (UCLouvain, LIDAM/ISBA)

Abstract

The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step in learning problems involving observations far away from the center. In the common situation that the components of the vector have different distributions, the rank transformation offers a convenient and robust way of standardizing data in order to build an empirical version of the angular measure based on the most extreme observations. We provide a functional asymptotic expansion for the empirical angular measure in the bivariate case based on the theory of weak convergence in the space of bounded functions. From the expansion, not only can the known asymptotic distribution of the empirical angular measure be recovered, it also enables to find expansions and weak limits for other statistics based on the associated empirical process or its quantile version.

Suggested Citation

  • Stéphane Lhaut & Johan Segers, 2024. "An Asymptotic Expansion of the Empirical Angular Measure for Bivariate Extremal Dependence," Springer Books, in: Matteo Barigozzi & Siegfried Hörmann & Davy Paindaveine (ed.), Recent Advances in Econometrics and Statistics, pages 187-208, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-61853-6_10
    DOI: 10.1007/978-3-031-61853-6_10
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    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:spr:sprchp:978-3-031-61853-6_10. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.