Translated Poisson approximation using exchangeable pair couplings

Details Translated Poisson approximation using exchangeable pair couplings Translated Poisson approximation using exchangeable pair couplings

2006-07-30

arxiv.org/abs/math/0607781v5

Annals of Applied Probability 2007, Vol. 17, No. 5,6, 1596-1614

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/105051607000000258 the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051607000000258

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.

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