On the Asymptotic Distribution of the Scan Statistic for Point Clouds

10/04/2019

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by   Andrew Ying, et al.

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We derive the large-sample distribution of several variants of the scan statistic applied to a point process on an interval, which can be applied to detect the presence of an anomalous interval with any length. The main ingredients in the proof are Kolmogorov's theorem, a Poisson approximation, and recent technical results by Kabluchko et al (2014).