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Compound Poisson approximation for the distribution of extremes


Barbour, A 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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 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:21 Nov 2017 14:22
Publisher:Applied Probability Trust
ISSN:0001-8678
Publisher DOI:https://doi.org/10.1239/aap/1019160958

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