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Rapid variation with remainder and rates of convergence

Published online by Cambridge University Press:  01 July 2016

J. Beirlant  and
E. Willekens
J. Beirlant*
Affiliation:
Katholieke Universiteit Leuven
E. Willekens*
Affiliation:
University of Technology, Eindhoven
*
∗Postal address: Faculteit Wetenschappen, Katholieke Universiteit Leuven, Dept. Wiskunde, Celestijinenlaan 200 B, B-3030 Leuven, Belgium.
∗∗Postal address: Department of Mathematics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
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Abstract

In this paper, we refine the concept of Γ-variation up to second order, and we give a characterization of this type of asymptotic behaviour. We apply our results to obtain uniform rates of convergence in the weak convergence of renormalised sample maxima to the double exponential distribution. In a second application we derive a rate of convergence result for the Hill estimator.

Keywords

REGULAR VARIATIONEXTREME VALUE THEORYHILL ESTIMATOR
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 4 , December 1990 , pp. 787 - 801
Copyright
Copyright © Applied Probability Trust 1990 

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