Bernoulli

  • Bernoulli
  • Volume 11, Number 6 (2005), 949-970.

Estimation of the extreme-value index and generalized quantile plots

J. Beirlant, G. Dierckx, and A. Guillou

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Abstract

In extreme-value analysis, a central topic is the adaptive estimation of the extreme-value index γ. Hitherto, most of the attention in this area has been devoted to the case γ>0, that is, when F ¯ is a regularly varying function with index -1/γ. In addition to the well-known Hill estimator, many other estimators are currently available. Among the most important are the kernel-type estimators and the weighted least-squares slope estimators based on the Pareto quantile plot or the Zipf plot, as reviewed by Csörgö and Viharos. Using an exponential regression model (ERM) for spacings between successive extreme order statistics, both Beirlant et al. and Feuerverger and Hall introduced bias-reduced estimators.

Article information

Source
Bernoulli, Volume 11, Number 6 (2005), 949-970.

Dates
First available in Project Euclid: 16 January 2006

Permanent link to this document
https://projecteuclid.org/euclid.bj/1137421635

Digital Object Identifier
doi:10.3150/bj/1137421635

Mathematical Reviews number (MathSciNet)
MR2188836

Zentralblatt MATH identifier
1123.62034

Keywords
bias extreme-value index least squares mean squared error quantile plots

Citation

Beirlant, J.; Dierckx, G.; Guillou, A. Estimation of the extreme-value index and generalized quantile plots. Bernoulli 11 (2005), no. 6, 949--970. doi:10.3150/bj/1137421635. https://projecteuclid.org/euclid.bj/1137421635


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