Moderate deviations in Poisson approximation: a first attempt

Louis H. Y. Chen; Xiao Fang; Qi-Man Shao

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arXiv · 1207.1605

Moderate deviations in Poisson approximation: a first attempt

Louis H. Y. Chen·Xiao Fang·Qi-Man Shao

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Abstract

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.

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Louis H. Y. Chen, Xiao Fang, Qi-Man Shao. 2013-06-20. Moderate deviations in Poisson approximation: a first attempt. https://arxiv.org/abs/1207.1605

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