Compound poisson approximation for the distribution of extremes

Article

Novak, S., Barbour, A. and Xia, A. 2002. Compound poisson approximation for the distribution of extremes. Advances in applied probability. 34 (1), pp. 223-240. https://doi.org/10.1239/aap/1019160958
TypeArticle
TitleCompound poisson approximation for the distribution of extremes
AuthorsNovak, S., Barbour, A. and Xia, A.
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.

PublisherApplied Probability Trust
JournalAdvances in applied probability
ISSN0001-8678
Publication dates
Print2002
Publication process dates
Deposited25 Mar 2009
Output statusPublished
Digital Object Identifier (DOI)https://doi.org/10.1239/aap/1019160958
LanguageEnglish
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