IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v57y2013i1p518-535.html
   My bibliography  Save this article

A simple generalisation of the Hill estimator

Author

Listed:
  • Fátima Brilhante, M.
  • Ivette Gomes, M.
  • Pestana, Dinis

Abstract

The classical Hill estimator of a positive extreme value index (EVI) can be regarded as the logarithm of the geometric mean, or equivalently the logarithm of the mean of order p=0, of a set of adequate statistics. A simple generalisation of the Hill estimator is now proposed, considering a more general mean of order p≥0 of the same statistics. Apart from the derivation of the asymptotic behaviour of this new class of EVI-estimators, an asymptotic comparison, at optimal levels, of the members of such class and other known EVI-estimators is undertaken. An algorithm for an adaptive estimation of the tuning parameters under play is also provided. A large-scale simulation study and an application to simulated and real data are developed.

Suggested Citation

  • Fátima Brilhante, M. & Ivette Gomes, M. & Pestana, Dinis, 2013. "A simple generalisation of the Hill estimator," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 518-535.
  • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:518-535
    DOI: 10.1016/j.csda.2012.07.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312002939
    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

    as
    1. Beran, Jan & Schell, Dieter, 2012. "On robust tail index estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3430-3443.
    2. Dekkers, A. L. M. & Dehaan, L., 1993. "Optimal Choice of Sample Fraction in Extreme-Value Estimation," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 173-195, November.
    3. Gomes, M. Ivette & Pestana, Dinis, 2007. "A Sturdy Reduced-Bias Extreme Quantile (VaR) Estimator," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 280-292, March.
    4. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    5. M. Ivette Gomes & Laurens de Haan & Lígia Henriques Rodrigues, 2008. "Tail index estimation for heavy-tailed models: accommodation of bias in weighted log-excesses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 31-52.
    6. M. Ivette Gomes & Cristina Miranda & Clara Viseu, 2007. "Reduced-bias tail index estimation and the jackknife methodology," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(2), pages 243-270.
    7. MacDonald, A. & Scarrott, C.J. & Lee, D. & Darlow, B. & Reale, M. & Russell, G., 2011. "A flexible extreme value mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2137-2157, June.
    8. Vandewalle, B. & Beirlant, J., 2006. "On univariate extreme value statistics and the estimation of reinsurance premiums," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 441-459, June.
    9. Gomes, M. Ivette & Neves, Cláudia, 2008. "Asymptotic comparison of the mixed moment and classical extreme value index estimators," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 643-653, April.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Gomes, M. Ivette & Henriques-Rodrigues, Lígia, 2016. "Competitive estimation of the extreme value index," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 128-135.
    2. Gomes, M. Ivette & Brilhante, M. Fátima & Caeiro, Frederico & Pestana, Dinis, 2015. "A new partially reduced-bias mean-of-order p class of extreme value index estimators," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 223-237.
    3. M. Ivette Gomes & Armelle Guillou, 2015. "Extreme Value Theory and Statistics of Univariate Extremes: A Review," International Statistical Review, International Statistical Institute, vol. 83(2), pages 263-292, August.
    4. Vygantas Paulauskas & Marijus Vaičiulis, 2017. "A class of new tail index estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 461-487, April.

    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:csdana:v:57:y:2013:i:1:p:518-535. 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: http://www.elsevier.com/locate/csda .

    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.