• 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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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.

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

First available in Project Euclid: 16 January 2006

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


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.

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