Exchangeable pairs and Poisson approximation
نویسندگان
چکیده
منابع مشابه
Exponential Approximation by Exchangeable Pairs and Spectral Graph Theory Running head: Exponential Approximation by Exchangeable Pairs
Running head: Exponential Approximation by Exchangeable Pairs Version of 4/7/06 By Sourav Chatterjee and Jason Fulman Abstract: A general Berry-Esseen bound is obtained for the exponential distribution using Stein’s method of exchangeable pairs. As an application, an error term is derived for Hora’s result that the spectrum of the Bernoulli-Laplace Markov chain has an exponential limit. This is...
متن کاملTranslated Poisson Approximation Using Exchangeable Pair Couplings
It is shown that the method of exchangeable pairs introduced by Stein (1986) 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 analysed by Rin...
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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...
متن کاملExponential approximation and Stein’s method of exchangeable pairs
The purpose of this paper is to further develop exponential approximation, using Stein’s method of exchangeable pairs. The first use of exchangeable pairs in exponential approximation was in the paper Chatterjee et al. (2011), which studied the spectrum of the Bernoulli-Laplace Markov chain. Unfortunately the results in Chatterjee et al. (2011), which use the Kolmogorov metric, are very complic...
متن کاملExponential approximation by exchangeable pairs and spectral graph theory
Running head: Exponential Approximation by Exchangeable Pairs Version of 4/7/06 By Sourav Chatterjee and Jason Fulman Abstract: A general Berry-Esseen bound is obtained for the exponential distribution using Stein’s method of exchangeable pairs. As an application, an error term is derived for Hora’s result that the spectrum of the Bernoulli-Laplace Markov chain has an exponential limit. This is...
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ژورنال
عنوان ژورنال: Probability Surveys
سال: 2005
ISSN: 1549-5787
DOI: 10.1214/154957805100000096