IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v47y1993i2p173-195.html
   My bibliography  Save this article

Optimal Choice of Sample Fraction in Extreme-Value Estimation

Author

Listed:
  • Dekkers, A. L. M.
  • Dehaan, L.

Abstract

We study the asymptotic bias of the moment estimator [gamma]n for the extreme-value index [gamma] [set membership, variant] 5 under quite natural and general conditions on the underlying distribution function. Furthermore the optimal choice for the sample franction in estimating [gamma] is considered by minimizing the mean squared error of [gamma]n - [gamma]. The results cover all three limiting types of extreme-value theory. The connection between statistics and regular variation and [Pi]-variation is handled in a systematic way.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:47:y:1993:i:2:p:173-195
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(83)71078-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.

    Citations

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


    Cited by:

    1. 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.
    2. Christian Schluter & Mark Trede, 2019. "Size distributions reconsidered," Econometric Reviews, Taylor & Francis Journals, vol. 38(6), pages 695-710, July.
    3. 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.
    4. 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.
    5. M. João Martins & M. Ivette Gopmes & M. Manuela Neves, 2004. "Averages of Hill estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 113-128, June.
    6. Gomes, M. Ivette & Henriques-Rodrigues, Lígia, 2016. "Competitive estimation of the extreme value index," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 128-135.
    7. 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.
    8. El-Aroui, Mhamed-Ali & Diebolt, Jean, 2002. "On the use of the peaks over thresholds method for estimating out-of-sample quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 453-475, June.
    9. 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.
    10. Tsourti, Zoi & Panaretos, John, 2003. "Extreme Value Index Estimators and Smoothing Alternatives: A Critical Review," MPRA Paper 6390, University Library of Munich, Germany.
    11. 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.
    12. 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.
    13. El Arrouchi Mohamed & Imlahi Abdelouahid, 2005. "Optimal choice of kn-records in the extreme value index estimation," Statistics & Risk Modeling, De Gruyter, vol. 23(2), pages 101-115, February.
    14. 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.
    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. Ana Ferreira & Casper G. de Vries, 2004. "Optimal Confidence Intervals for the Tail Index and High Quantiles," Tinbergen Institute Discussion Papers 04-090/2, Tinbergen Institute.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. Peng, L., 1998. "Asymptotically unbiased estimators for the extreme-value index," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 107-115, June.
    22. Djamel Meraghni & Abdelhakim Necir, 2007. "Estimating the Scale Parameter of a Lévy-stable Distribution via the Extreme Value Approach," Methodology and Computing in Applied Probability, Springer, vol. 9(4), pages 557-572, December.
    23. Necir, Abdelhakim & Meraghni, Djamel, 2009. "Empirical estimation of the proportional hazard premium for heavy-tailed claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 49-58, August.
    24. Laurens F.M. de Haan & Liang Peng & T.T. Pereira, 1997. "A Bootstrap-based Method to Achieve Optimality in Estimating the Extreme-value Index," Tinbergen Institute Discussion Papers 97-099/4, Tinbergen Institute.

    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:jmvana:v:47:y:1993:i:2:p:173-195. 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: 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.