MODERATE DEVIATIONS IN POISSON APPROXIMATION: A FIRST ATTEMPT

Poisson approximation using Stein's method has been extensively studied in the literature. The main focus has been on bounding the total variation distance. This paper is a first attempt on moderate deviations in Poisson approximation for right-tail probabilities of sums of dependent indicators...

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Bibliographic Details
Published in:Statistica Sinica 2013-10, Vol.23 (4), p.1523-1540
Main Authors: Chen, Louis H. Y., Fang, Xiao, Shao, Qi-Man
Format: Article
Language:English
Subjects:
Approximation
Integers
Probabilities
Random variables
Online Access:Get full text
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Summary:Poisson approximation using Stein's method has been extensively studied in the literature. The main focus has been on bounding the total variation distance. This paper is a first attempt on moderate deviations in Poisson approximation for right-tail probabilities of sums of dependent indicators. We obtain results under certain general conditions for local dependence as well as for size-bias coupling. These results are then applied to independent indicators, 2-runs, and the matching problem.
ISSN:1017-0405
1996-8507
DOI:10.5705/ss.2012.203s