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On exceedances of high levels

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  • Novak, S.Y.
  • Xia, A.
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    Abstract

    The distribution of the excess process describing heights of extreme values can be approximated by the distribution of a Poisson cluster process. An estimate of the accuracy of such an approximation has been derived in [4] in terms of the Wasserstein distance. The paper presents a sharper estimate established in terms of the stronger total variation distance. We derive also a new bound to the accuracy of negative Binomial approximation to the distribution of the number of exceedances.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304414911002262
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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 2 ()
    Pages: 582-599

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:2:p:582-599

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    Related research

    Keywords: Extreme values; Poisson cluster process; Compound Poisson approximation; Negative Binomial approximation; Total variation distance;

    References

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    1. Novak, S. Y., 2003. "On the accuracy of multivariate compound Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 62(1), pages 35-43, March.
    2. Roos, Bero, 1999. "On the Rate of Multivariate Poisson Convergence," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 120-134, April.
    3. Novak, S. Y., 2002. "Multilevel clustering of extremes," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 59-75, January.
    4. Roos, Bero, 2001. "Sharp constants in the Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 155-168, April.
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