IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/6390.html
   My bibliography  Save this paper

Extreme Value Index Estimators and Smoothing Alternatives: A Critical Review

Author

Listed:
  • Tsourti, Zoi
  • Panaretos, John

Abstract

Extreme-value theory and corresponding analysis is an issue extensively applied in many different fields. The central point of this theory is the estimation of a parameter γ, known as the extreme-value index. In this paper we review several extreme-value index estimators, ranging from the oldest ones to the most recent developments. Moreover, some smoothing and robustifying procedures of these estimators are presented.

Suggested Citation

  • Tsourti, Zoi & Panaretos, John, 2003. "Extreme Value Index Estimators and Smoothing Alternatives: A Critical Review," MPRA Paper 6390, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:6390
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/6390/1/MPRA_paper_6390.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Armelle Guillou & Peter Hall, 2001. "A diagnostic for selecting the threshold in extreme value analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 293-305.
    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. 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.
    4. Jón Daníelsson & Casper G. de Vries, 1998. "Beyond the Sample: Extreme Quantile and Probability Estimation," Tinbergen Institute Discussion Papers 98-016/2, Tinbergen Institute.
    5. Olivier V. Pictet & Michel M. Dacorogna & Ulrich A. Muller, 1996. "Hill, Bootstrap and Jackknife Estimators for Heavy Tails," Working Papers 1996-12-10, Olsen and Associates.
    6. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
    7. Peng, L., 1998. "Asymptotically unbiased estimators for the extreme-value index," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 107-115, June.
    8. Paul Embrechts & Sidney Resnick & Gennady Samorodnitsky, 1999. "Extreme Value Theory as a Risk Management Tool," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(2), pages 30-41.
    9. M. I. Barão & J. A. Tawn, 1999. "Extremal analysis of short series with outliers: sea‐levels and athletics records," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(4), pages 469-487.
    10. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
    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. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    2. Ivanilda Cabral & Frederico Caeiro & M. Ivette Gomes, 2022. "On the comparison of several classical estimators of the extreme value index," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(1), pages 179-196, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tsourti, Zoi & Panaretos, John, 2004. "Extreme-value analysis of teletraffic data," Computational Statistics & Data Analysis, Elsevier, vol. 45(1), pages 85-103, February.
    2. Wager, Stefan, 2014. "Subsampling extremes: From block maxima to smooth tail estimation," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 335-353.
    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. Ana-Maria Gavril, 2009. "Exchange Rate Risk: Heads or Tails," Advances in Economic and Financial Research - DOFIN Working Paper Series 35, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
    5. Neves, Claudia & Fraga Alves, M. I., 2004. "Reiss and Thomas' automatic selection of the number of extremes," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 689-704, November.
    6. Małgorzata Just & Krzysztof Echaust, 2021. "An Optimal Tail Selection in Risk Measurement," Risks, MDPI, vol. 9(4), pages 1-16, April.
    7. Koning, A.J. & Peng, L., 2005. "Goodness-of-fit tests for a heavy tailed distribution," Econometric Institute Research Papers EI 2005-44, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    8. Krajina, A., 2010. "An M-estimator of multivariate tail dependence," Other publications TiSEM 66518e07-db9a-4446-81be-c, Tilburg University, School of Economics and Management.
    9. Lee, J. & Fan, Y. & Sisson, S.A., 2015. "Bayesian threshold selection for extremal models using measures of surprise," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 84-99.
    10. Holger Drees & Laurens F.M. de Haan & Sidney Resnick, 1998. "How to make a Hill Plot," Tinbergen Institute Discussion Papers 98-090/4, Tinbergen Institute.
    11. Danielsson, J. & de Haan, L. & Peng, L. & de Vries, C. G., 2001. "Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 226-248, February.
    12. 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.
    13. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
    14. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    15. Brahimi, Brahim & Meraghni, Djamel & Necir, Abdelhakim & Zitikis, Ričardas, 2011. "Estimating the distortion parameter of the proportional-hazard premium for heavy-tailed losses," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 325-334.
    16. Gencay, Ramazan & Selcuk, Faruk & Ulugulyagci, Abdurrahman, 2003. "High volatility, thick tails and extreme value theory in value-at-risk estimation," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 337-356, October.
    17. Goran Andjelic & Ivana Milosev & Vladimir Djakovic, 2010. "Extreme Value Theory In Emerging Markets," Economic Annals, Faculty of Economics and Business, University of Belgrade, vol. 55(185), pages 63-106, April - J.
    18. Raymond Knott & Marco Polenghi, 2006. "Assessing central counterparty margin coverage on futures contracts using GARCH models," Bank of England working papers 287, Bank of England.
    19. Madhusudan Karmakar, 2013. "Estimation of tail‐related risk measures in the Indian stock market: An extreme value approach," Review of Financial Economics, John Wiley & Sons, vol. 22(3), pages 79-85, September.
    20. Weshah Razzak, "undated". "On the GCC Currency Union," API-Working Paper Series 0910, Arab Planning Institute - Kuwait, Information Center.

    More about this item

    Keywords

    Extreme value index; Semi-parametric estimation; Smoothing modification;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    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:pra:mprapa:6390. 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.

    If CitEc recognized a bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.