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Asymptotic results for jump probabilities associated to the multiple scan statistic

Author

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  • Markos V. Koutras

    (University of Piraeus)

  • Demetrios P. Lyberopoulos

    (University of Piraeus)

Abstract

The concept of pattern arises in many applications comprising experimental trials with two or more possible outcomes in each trial. A binary scan of type r / k is a special pattern referring to success–failure strings of fixed length k that contain at least r-successes, where r, k are positive integers with $$r\le k$$ r ≤ k . The multiple scan statistic $$W_{t,k,r}$$ W t , k , r is defined as the enumerating random variable for the overlapping moving windows occurring until trial t which include a scan of type r / k. In the present work, we consider a sequence of independent binary trials with not necessarily equal probabilities of success and develop upper bounds for the probability of the event that the multiple scan statistic will perform a jump from $$\ell $$ ℓ to $$\ell +1$$ ℓ + 1 (where $$\ell $$ ℓ is a nonnegative integer) in a finite time horizon.

Suggested Citation

  • Markos V. Koutras & Demetrios P. Lyberopoulos, 2018. "Asymptotic results for jump probabilities associated to the multiple scan statistic," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 951-968, October.
    • Handle: RePEc:spr:aistmt:v:70:y:2018:i:5:d:10.1007_s10463-017-0621-1
    DOI: 10.1007/s10463-017-0621-1
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    References listed on IDEAS

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