Compound poisson approximation for the distribution of extremes

Novak, Serguei and Barbour, A. D. and Xia, Aihua (2002) Compound poisson approximation for the distribution of extremes. Advances in applied probability, 34 (1). pp. 223-240. ISSN 0001-8678

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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.

Item Type:Article
Research Areas:Middlesex University Schools and Centres > School of Science and Technology > Design Engineering and Mathematics
Citations on ISI Web of Science:4
ID Code:1709
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Deposited On:25 Mar 2009 12:01
Last Modified:07 Nov 2014 16:27

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