The Annals of Applied Probability

Translated Poisson approximation using exchangeable pair couplings

Adrian Röllin

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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.

Article information

Source
Ann. Appl. Probab., Volume 17, Number 5/6 (2007), 1596-1614.

Dates
First available in Project Euclid: 3 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1191419177

Digital Object Identifier
doi:10.1214/105051607000000258

Mathematical Reviews number (MathSciNet)
MR2358635

Zentralblatt MATH identifier
1143.60020

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 62E20: Asymptotic distribution theory

Keywords
Translated Poisson distribution Stein’s method exchangeable pairs local limit theorem

Citation

Röllin, Adrian. Translated Poisson approximation using exchangeable pair couplings. Ann. Appl. Probab. 17 (2007), no. 5/6, 1596--1614. doi:10.1214/105051607000000258. https://projecteuclid.org/euclid.aoap/1191419177


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