Open Access
dec 2005 Estimation of the extreme-value index and generalized quantile plots
J. Beirlant, G. Dierckx, A. Guillou
Bernoulli 11(6): 949-970 (dec 2005). DOI: 10.3150/bj/1137421635


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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J. Beirlant. G. Dierckx. A. Guillou. "Estimation of the extreme-value index and generalized quantile plots." Bernoulli 11 (6) 949 - 970, dec 2005.


Published: dec 2005
First available in Project Euclid: 16 January 2006

zbMATH: 1123.62034
MathSciNet: MR2188836
Digital Object Identifier: 10.3150/bj/1137421635

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

Rights: Copyright © 2005 Bernoulli Society for Mathematical Statistics and Probability

Vol.11 • No. 6 • dec 2005
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