IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/99cf59.html
   My bibliography  Save this paper

Tail Probability via Tube Formula and Euler Characteristic Method when Critical Radius is Zero

Author

Listed:
  • Akimichi Takemura

    (Faculty of Economics, University of Tokyo)

  • Satoshi Kuriki

    (The Institute of Statistical Mathematics)

Abstract

In Takemura and Kuriki(1999b) we have established that the tube formula and the Euler characteristic method give identical and valid asymptotic expansion of tail probability of the maximum of Gaussian random field when the random field has finite Karhunen-Loeve expansion and the index set has positive critical radius. The purpose of this paper is to show that the positiveness of the critical radius is an essential condition. Namely, we prove that if the critical radius is zero, only the main term is valid and other higher order terms are generally not valid in the formal asymptotic expansion based on the tube formula or the Euler characteristic method. Our examples show that index sets with zero critical radius are commonly used in statistics.

Suggested Citation

  • Akimichi Takemura & Satoshi Kuriki, 1999. "Tail Probability via Tube Formula and Euler Characteristic Method when Critical Radius is Zero," CIRJE F-Series CIRJE-F-59, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:99cf59
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/99/cf59/contents.htm
    Download Restriction: no
    ---><---

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:tky:fseres:99cf59. 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: CIRJE administrative office (email available below). General contact details of provider: https://edirc.repec.org/data/ritokjp.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.