The Annals of Applied Probability

Poisson approximation for two scan statistics with rates of convergence

Xiao Fang and David Siegmund

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1472745462

Digital Object Identifier
doi:10.1214/15-AAP1150

Mathematical Reviews number (MathSciNet)
MR3543900

Zentralblatt MATH identifier
1352.60032

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

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

Citation

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. https://projecteuclid.org/euclid.aoap/1472745462


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