Asymptotic results for jump probabilities associated to the multiple scan statistic

Markos V. Koutras () and Demetrios P. Lyberopoulos ()
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Markos V. Koutras: University of Piraeus
Demetrios P. Lyberopoulos: University of Piraeus

Annals of the Institute of Statistical Mathematics, 2018, vol. 70, issue 5, No 1, 968 pages

Abstract: 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.

Keywords: Multiple scan statistic; Upper bound; Demisubmartingale; N-demisupermartingale; Demimartingale (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10463-017-0621-1

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