The Annals of Probability

Von Mises Conditions Revisited

Michael Falk and Frank Marohn

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Abstract

It is shown that the rate of convergence in the von Mises conditions of extreme value theory determines the distance of the underlying distribution function $F$ from a generalized Pareto distribution. The distance is measured in terms of the pertaining densities with the limit being ultimately attained if and only if $F$ is ultimately a generalized Pareto distribution. Consequently, the rate of convergence of the extremes in an iid sample, whether in terms of the distribution of the largest order statistics or of corresponding empirical truncated point processes, is determined by the rate of convergence in the von Mises condition. We prove that the converse is also true.

Article information

Source
Ann. Probab., Volume 21, Number 3 (1993), 1310-1328.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989120

Digital Object Identifier
doi:10.1214/aop/1176989120

Mathematical Reviews number (MathSciNet)
MR1235418

Zentralblatt MATH identifier
0778.60040

JSTOR
links.jstor.org

Subjects
Primary: 60G70: Extreme value theory; extremal processes
Secondary: 62G30: Order statistics; empirical distribution functions

Keywords
Von Mises conditions extreme value theory extreme value distribution extreme order statistics generalized Pareto distribution rate of convergence empirical point process

Citation

Falk, Michael; Marohn, Frank. Von Mises Conditions Revisited. Ann. Probab. 21 (1993), no. 3, 1310--1328. doi:10.1214/aop/1176989120. https://projecteuclid.org/euclid.aop/1176989120


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