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Rate of Poisson approximation of the number of exceedances of nonstationary normal sequences

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  • Hüsler, J.
  • Kratz, M.

Abstract

It is known that the partial maximum of nonstationary Gaussian sequences converges in distribution and that the number of exceedances of a boundary is asymptotically a Poisson random variable, under certain restrictions. We investigate the rate of Poisson approximation for the number of exceedances. We generalize the result known in the stationary case, showing that the given bound of the rate depends on the largest positive auto-correlation value (less than 1) and the lowest values of the nonconstant boundary. We show that for special cases this bound cannot be improved.

Suggested Citation

  • Hüsler, J. & Kratz, M., 1995. "Rate of Poisson approximation of the number of exceedances of nonstationary normal sequences," Stochastic Processes and their Applications, Elsevier, vol. 55(2), pages 301-313, February.
    • Handle: RePEc:eee:spapps:v:55:y:1995:i:2:p:301-313
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    References listed on IDEAS

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    1. Smith, Richard L., 1988. "Extreme value theory for dependent sequences via the stein-chen method of poisson approximation," Stochastic Processes and their Applications, Elsevier, vol. 30(2), pages 317-327, December.
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    Cited by:

    1. Hashorva, Enkelejd & Hüsler, Jürg, 2002. "Remarks on compound Poisson approximation of Gaussian random sequences," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 1-8, March.

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