One Dimensional Discrete Scan Statistics for Dependent Models and Some Related Problems

Alexandru Amarioarei and Cristian Preda
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Alexandru Amarioarei: Faculty of Mathematics and Computer Science, University of Bucharest, 010014 Bucharest, Romania
Cristian Preda: Laboratoire de Mathématiques Paul Painlevé, University of Lille, 59655 Villeneuve d’Ascq, France

Mathematics, 2020, vol. 8, issue 4, 1-11

Abstract: The one dimensional discrete scan statistic is considered over sequences of random variables generated by block factor dependence models. Viewed as a maximum of an 1-dependent stationary sequence, the scan statistics distribution is approximated with accuracy and sharp bounds are provided. The longest increasing run statistics is related to the scan statistics and its distribution is studied. The moving average process is a particular case of block factor and the distribution of the associated scan statistics is approximated. Numerical results are presented.

Keywords: scan statistics; 1-dependence; runs; approximation; simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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