Compound Poisson approximation for the distribution of extremes
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.
Permanent link to this document: http://projecteuclid.org/euclid.aap/1019160958
Digital Object Identifier: doi:10.1239/aap/1019160958
Mathematical Reviews number (MathSciNet): MR1895339
Zentralblatt MATH identifier: 1005.60065