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Refined Pickands Estimators of the Extreme Value Index

Holger Drees
The Annals of Statistics
Vol. 23, No. 6 (Dec., 1995), pp. 2059-2080
Stable URL: http://www.jstor.org/stable/2242785
Page Count: 22
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Refined Pickands Estimators of the Extreme Value Index
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Abstract

Consider a distribution function that belongs to the weak domain of attraction of an extreme value distribution. The extreme value index β will be estimated by mixtures of Pickands estimators, where the weights are generated by a probability measure which satisfies a certain integrability condition. We prove a functional limit theorem for a process of Pickands estimators and asymptotic normality of the refined Pickands estimator. For negative β the new estimator is asymptotically superior to previously defined estimators. A simulation study also demonstrates the good small-sample performance. In particular, the estimator proves to be robust against an inappropriate choice of the number of upper order statistics used for estimation.

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