The Annals of Applied Probability

Poisson approximation for two scan statistics with rates of convergence

Xiao Fang and David Siegmund

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As an application of Stein’s method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detecting local signals in sequences of independent random variables subject to possible change-points. Our formulation deals simultaneously with ordinary and with large deviations.

Article information

Ann. Appl. Probab., Volume 26, Number 4 (2016), 2384-2418.

Received: March 2014
Revised: May 2015
First available in Project Euclid: 1 September 2016

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 62E20: Asymptotic distribution theory
Secondary: 62L10: Sequential analysis

Stein’s method Poisson approximation total variation distance relative error rate of convergence scan statistics change-point analysis exponential family


Fang, Xiao; Siegmund, David. Poisson approximation for two scan statistics with rates of convergence. Ann. Appl. Probab. 26 (2016), no. 4, 2384--2418. doi:10.1214/15-AAP1150.

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