Statistica Sinica 23 (2013), 1523-1540

MODERATE DEVIATIONS IN POISSON APPROXIMATION:

A FIRST ATTEMPT

Louis H. Y. Chen$^1$, Xiao Fang$^{1,2}$ and Qi-Man Shao$^3$

$^1$National University of Singapore, $^2$Stanford University and

$^3$Chinese University of Hong Kong

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.

Key words and phrases: Local dependence, moderate deviations, Poisson approximation, size-bias coupling, Stein's method.