The Annals of Probability

Second-order regular variation and rates of convergence in extreme-value theory

Sidney Resnick and Laurens de Haan

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Abstract

Rates of convergence of the distribution of the extreme order statistic to its limit distribution are given in the uniform metric and the total variation metric. A second-order regular variation condition is imposed by supposing a von Mises type condition which allows a unified treatment. Rates are constructed from the parameters of the second-order regular variation condition. Some connections with Poisson processes are discussed.

Article information

Source
Ann. Probab., Volume 24, Number 1 (1996), 97-124.

Dates
First available in Project Euclid: 15 January 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1042644709

Digital Object Identifier
doi:10.1214/aop/1042644709

Mathematical Reviews number (MathSciNet)
MR1387628

Zentralblatt MATH identifier
0862.60039

Citation

de Haan, Laurens; Resnick, Sidney. Second-order regular variation and rates of convergence in extreme-value theory. Ann. Probab. 24 (1996), no. 1, 97--124. doi:10.1214/aop/1042644709. https://projecteuclid.org/euclid.aop/1042644709


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