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Remarks on compound Poisson approximation of Gaussian random sequences

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  • Hashorva, Enkelejd
  • Hüsler, Jürg

Abstract

Let {Xi, i[greater-or-equal, slanted]1} be a sequence of m-dependent stationary standard Gaussian random variables and some positive constants. In this note we generalise results of Raab (Extremes 1(3) (1999) 29.), who considered compound Poisson approximation for Wn=[summation operator]i=1n1{Xi>un} the number of exceedances above the level un. More precisely, the main result concerns an upper asymptotic bound for the total variational distance dTV(Wn,CP([lambda]*)) where with 2[less-than-or-equals, slant]r[less-than-or-equals, slant]2m and are independent Poisson random variables.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:stapro:v:57:y:2002:i:1:p:1-8
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    References listed on IDEAS

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    1. Gnedin, Alexander V., 1998. "Records from a multivariate normal sample," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 11-15, July.
    2. Barbour, A. D. & Utev, Sergey, 1999. "Compound Poisson approximation in total variation," Stochastic Processes and their Applications, Elsevier, vol. 82(1), pages 89-125, July.
    3. 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.
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    Cited by:

    1. Hashorva, Enkelejd, 2010. "On the residual dependence index of elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1070-1078, July.

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