IDEAS home Printed from https://ideas.repec.org/a/bla/anzsta/v46y2004i2p305-312.html
   My bibliography  Save this article

Estimating the First‐ and Second‐Order Parameters of a Heavy‐Tailed Distribution

Author

Listed:
  • Liang Peng
  • Yongcheng Qi

Abstract

This paper suggests censored maximum likelihood estimators for the first‐ and second‐order parameters of a heavy‐tailed distribution by incorporating the second‐order regular variation into the censored likelihood function. This approach is different from the bias‐reduced maximum likelihood method proposed by Feuerverger and Hall in 1999. The paper derives the joint asymptotic limit for the first‐ and second‐order parameters under a weaker assumption. The paper also demonstrates through a simulation study that the suggested estimator for the first‐order parameter is better than the estimator proposed by Feuerverger and Hall although these two estimators have the same asymptotic variances.

Suggested Citation

  • Liang Peng & Yongcheng Qi, 2004. "Estimating the First‐ and Second‐Order Parameters of a Heavy‐Tailed Distribution," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 46(2), pages 305-312, June.
    • Handle: RePEc:bla:anzsta:v:46:y:2004:i:2:p:305-312
    DOI: 10.1111/j.1467-842X.2004.00331.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-842X.2004.00331.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-842X.2004.00331.x?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
    ---><---

    Citations

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


    Cited by:

    1. Gomes, M. Ivette & Pestana, Dinis & Caeiro, Frederico, 2009. "A note on the asymptotic variance at optimal levels of a bias-corrected Hill estimator," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 295-303, February.
    2. Arthur Charpentier & Emmanuel Flachaire, 2019. "Pareto Models for Top Incomes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02145024, HAL.
    3. Arthur Charpentier & Emmanuel Flachaire, 2021. "Pareto Models for Risk Management," Dynamic Modeling and Econometrics in Economics and Finance, in: Gilles Dufrénot & Takashi Matsuki (ed.), Recent Econometric Techniques for Macroeconomic and Financial Data, pages 355-387, Springer.
    4. Rassoul, Abdelaziz, 2013. "Kernel-type estimator of the conditional tail expectation for a heavy-tailed distribution," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 698-703.

    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:bla:anzsta:v:46:y:2004:i:2:p:305-312. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=1369-1473 .

    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.