IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v80y2010i7-8p739-746.html
   My bibliography  Save this article

Comparing extreme models when the sign of the extreme value index is known

Author

Listed:
  • Li, Deyuan
  • Peng, Liang

Abstract

In the literature on analyzing extremes, both generalized Pareto distributions and Pareto distributions are employed to infer the tail of a distribution with a known positive extreme value index. Similar studies exist for a known negative extreme value index. Intuitively, one should not employ the generalized Pareto distribution in the case of knowing the sign of the extreme value index. In this work, we show that fitting a generalized Pareto distribution is equivalent to the model in Hall (1982) in the case of a negative extreme value index, in both improving the rate of convergence and including the bias term of the asymptotic results of that reference. When the extreme value index is known to be positive, we show that fitting a generalized Pareto distribution may be preferred in some cases determined by a so-called second-order parameter and the extreme value index itself.

Suggested Citation

  • Li, Deyuan & Peng, Liang, 2010. "Comparing extreme models when the sign of the extreme value index is known," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 739-746, April.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:7-8:p:739-746
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(10)00009-X
    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. L. De Haan & L. Peng, 1998. "Comparison of tail index estimators," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(1), pages 60-70, March.
    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. Matheus Henrique Junqueira Saldanha & Adriano Kamimura Suzuki, 2023. "On dealing with the unknown population minimum in parametric inference," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 509-535, September.

    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. Andrey Pepelyshev & Anatoly Zhigljavsky & Antanas Žilinskas, 2018. "Performance of global random search algorithms for large dimensions," Journal of Global Optimization, Springer, vol. 71(1), pages 57-71, May.
    2. 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.
    3. 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.
    4. Christian Schluter, 2021. "On Zipf’s law and the bias of Zipf regressions," Empirical Economics, Springer, vol. 61(2), pages 529-548, August.
    5. Ahmad Aboubacrène Ag & Deme El Hadji & Diop Aliou & Girard Stéphane, 2019. "Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions," Dependence Modeling, De Gruyter, vol. 7(1), pages 394-417, January.
    6. Igor Fedotenkov, 2013. "A bootstrap method to test for the existence of finite moments," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 315-322, June.
    7. Giulio Bottazzi & Davide Pirino & Federico Tamagni, 2015. "Zipf law and the firm size distribution: a critical discussion of popular estimators," Journal of Evolutionary Economics, Springer, vol. 25(3), pages 585-610, July.
    8. Ghosh, Souvik & Resnick, Sidney, 2010. "A discussion on mean excess plots," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1492-1517, August.
    9. Chao Huang & Jin-Guan Lin & Yan-Yan Ren, 2012. "Statistical Inferences for Generalized Pareto Distribution Based on Interior Penalty Function Algorithm and Bootstrap Methods and Applications in Analyzing Stock Data," Computational Economics, Springer;Society for Computational Economics, vol. 39(2), pages 173-193, February.
    10. Jan Beran & Dieter Schell & Milan Stehlík, 2014. "The harmonic moment tail index estimator: asymptotic distribution and robustness," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 193-220, February.
    11. Wagner, Niklas & Marsh, Terry A., 2005. "Measuring tail thickness under GARCH and an application to extreme exchange rate changes," Journal of Empirical Finance, Elsevier, vol. 12(1), pages 165-185, January.
    12. Fang, Wen & Wang, Jun, 2013. "Fluctuation behaviors of financial time series by a stochastic Ising system on a Sierpinski carpet lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 4055-4063.
    13. P. Lai & Stephen Lee, 2013. "Estimation of central shapes of error distributions in linear regression problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 105-124, February.
    14. Geluk, J. L. & Peng, Liang, 2000. "An adaptive optimal estimate of the tail index for MA(l) time series," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 217-227, February.
    15. 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.
    16. 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.
    17. Frederico Caeiro & M. Ivette Gomes & Björn Vandewalle, 2014. "Semi-Parametric Probability-Weighted Moments Estimation Revisited," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 1-29, March.
    18. Fendel, Ralf & Neumann, Christian, 2021. "Tail risk in the European sovereign bond market during the financial crises: Detecting the influence of the European Central Bank," Global Finance Journal, Elsevier, vol. 50(C).
    19. Hsieh, Ping-Hung, 2002. "An exploratory first step in teletraffic data modeling: evaluation of long-run performance of parameter estimators," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 263-283, August.
    20. Haeusler, E. & Segers, J., 2005. "Assessing Confidence Intervals for the Tail Index by Edgeworth Expansions for the Hill Estimator," Other publications TiSEM e635c476-8fa8-4f16-8760-2, Tilburg University, School of Economics and Management.

    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:eee:stapro:v:80:y:2010:i:7-8:p:739-746. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.