Translated Poisson approximation using exchangeable pair couplings
Abstract
It is shown that the method of exchangeable pairs introduced by Stein [Approximate Computation of Expectations (1986) IMS, Hayward, CA] for normal approximation can effectively be used for translated Poisson approximation. Introducing an additional smoothness condition, one can obtain approximation results in total variation and also in a local limit metric. The result is applied, in particular, to the anti-voter model on finite graphs as analyzed by Rinott and Rotar [Ann. Appl. Probab. 7 (1997) 1080--1105], obtaining the same rate of convergence, but now for a stronger metric.
Keywords
Cite
@article{arxiv.math/0607781,
title = {Translated Poisson approximation using exchangeable pair couplings},
author = {Adrian Röllin},
journal= {arXiv preprint arXiv:math/0607781},
year = {2010}
}
Comments
Published in at http://dx.doi.org/10.1214/105051607000000258 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)