Header

UZH-Logo

Maintenance Infos

Compound Poisson approximation for the distribution of extremes


Barbour, Andrew D; Novak, S; Xia, A (2002). Compound Poisson approximation for the distribution of extremes. Advances in Applied Probability, 34(1):223-240.

Abstract

Empirical point processes of exceedances play an important role in extreme value theory, and their limiting behaviour has been extensively studied. Here, we provide explicit bounds on the accuracy of approximating an exceedance process by a compound Poisson or Poisson cluster process, in terms of a Wasserstein metric that is generally more suitable for the purpose than the total variation metric. The bounds only involve properties of the finite, empirical sequence that is under consideration, and not of any limiting process. The argument uses Bernstein blocks and Lindeberg's method of compositions.

Abstract

Empirical point processes of exceedances play an important role in extreme value theory, and their limiting behaviour has been extensively studied. Here, we provide explicit bounds on the accuracy of approximating an exceedance process by a compound Poisson or Poisson cluster process, in terms of a Wasserstein metric that is generally more suitable for the purpose than the total variation metric. The bounds only involve properties of the finite, empirical sequence that is under consideration, and not of any limiting process. The argument uses Bernstein blocks and Lindeberg's method of compositions.

Statistics

Citations

Dimensions.ai Metrics
9 citations in Web of Science®
13 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

125 downloads since deposited on 07 Apr 2010
14 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:Extreme values, point processes, exceedances, compound Poisson process, total variation metric, coupling
Language:English
Date:2002
Deposited On:07 Apr 2010 10:32
Last Modified:08 Jul 2024 03:30
Publisher:Cambridge University Press
ISSN:0001-8678
OA Status:Green
Publisher DOI:https://doi.org/10.1239/aap/1019160958
  • Content: Submitted Version
  • Language: English
  • Description: Preprint