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.

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)

References in corpus (3)

• Stein's method and the zero bias transformation with application to simple random sampling
• Exchangeable pairs and Poisson approximation
• Zero biasing and a discrete central limit theorem

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