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Approximations of the boundary crossing probabilities for the maximum of moving weighted sums

Author

Listed:
  • Jack Noonan

    (Cardiff University)

  • Anatoly Zhigljavsky

    (Cardiff University)

Abstract

We study approximations of boundary crossing probabilities for the maximum of moving weighted sums of i.i.d. random variables. We consider a particular case of weights obtained from a trapezoidal weight function which, under certain parameter choices, can also result in an unweighted sum. We demonstrate that the approximations based on classical results of extreme value theory provide some scope for improvement, particularly for a range of values required in practical applications.

Suggested Citation

  • Jack Noonan & Anatoly Zhigljavsky, 2018. "Approximations of the boundary crossing probabilities for the maximum of moving weighted sums," Statistical Papers, Springer, vol. 59(4), pages 1325-1337, December.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:4:d:10.1007_s00362-018-1015-z
    DOI: 10.1007/s00362-018-1015-z
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    Cited by:

    1. Noonan, Jack & Zhigljavsky, Anatoly, 2019. "Approximating Shepp’s constants for the Slepian process," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 21-31.

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