On the Asymptotic Distribution of the Scan Statistic for Empirical Distributions
Statistics Theory
2020-03-26 v2 Probability
Statistics Theory
Abstract
We investigate the asymptotic behavior of several variants of the scan statistic applied to empirical distributions, which can be applied to detect the presence of an anomalous interval with any length. Of particular interest is Studentized scan statistic that is preferable in practice. The main ingredients in the proof are Kolmogorov's theorem, a Poisson approximation, and recent technical results by Kabluchko et al (2014).
Keywords
Cite
@article{arxiv.1910.01809,
title = {On the Asymptotic Distribution of the Scan Statistic for Empirical Distributions},
author = {Andrew Ying and Wen-Xin Zhou},
journal= {arXiv preprint arXiv:1910.01809},
year = {2020}
}