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Translated Poisson approximation using exchangeable pair couplings


Röllin, A (2007). Translated Poisson approximation using exchangeable pair couplings. Annals of Applied Probability, 17(5-6):1596-1614.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Uncontrolled Keywords:Translated Poisson distribution, Stein’s method, exchangeable pairs, local limit theorem
Language:English
Date:2007
Deposited On:03 Nov 2009 08:59
Last Modified:03 May 2024 01:37
Publisher:Institute of Mathematical Statistics
ISSN:1050-5164
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1214/105051607000000258
Related URLs:http://arxiv.org/abs/math/0607781
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