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The empirical distribution function as a tail estimator

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  • J.H.J. Einmahl

Abstract

It is shown that the empirical distribution function performs well in tail estimation. Consistency as well as the relative error are considered. The results hold true without any condition on the theoretical distribution function.

Suggested Citation

  • J.H.J. Einmahl, 1990. "The empirical distribution function as a tail estimator," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 44(2), pages 79-82, June.
    • Handle: RePEc:bla:stanee:v:44:y:1990:i:2:p:79-82
    DOI: 10.1111/j.1467-9574.1990.tb01528.x
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    Cited by:

    1. Di Bernardino, Elena & Maume-Deschamps, Véronique & Prieur, Clémentine, 2013. "Estimating a bivariate tail: A copula based approach," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 81-100.
    2. Rootzén, Holger, 2009. "Weak convergence of the tail empirical process for dependent sequences," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 468-490, February.
    3. Remigijus Leipus & Anne Philippe & Vytautė Pilipauskaitė & Donatas Surgailis, 2020. "Estimating Long Memory in Panel Random‐Coefficient AR(1) Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 520-535, July.
    4. Francis X. Diebold & Til Schuermann & John D. Stroughair, 1998. "Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management," Center for Financial Institutions Working Papers 98-10, Wharton School Center for Financial Institutions, University of Pennsylvania.
    5. Geluk, J. & de Haan, L. & Resnick, S. & Starica, C., 1997. "Second-order regular variation, convolution and the central limit theorem," Stochastic Processes and their Applications, Elsevier, vol. 69(2), pages 139-159, September.
    6. Abdelaati Daouia & Laurent Gardes & Stéphane Girard & Alexandre Lekina, 2011. "Kernel estimators of extreme level curves," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 311-333, August.

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