Moderate deviations in Poisson approximation: a first attempt

2012/07/06 by Louis H. Y. Chen, Xiao Fang, Chen, Louis H. Y. +3
Mathematics · #60F10 (Primary) 60F05 (Secondary) #Advanced Combinatorial Mathematics #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #math.PR #msc:60F05 #msc:60F10

paper · pdf · doi:10.48550/arxiv.1207.1605

21 pages

openalex publication_date 2012/07/06 · arxiv created 2013/06/20 · arxiv updated 2013/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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