Poisson Approximation Using Exchangeable Pair Couplings
نویسندگان
چکیده
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.
منابع مشابه
Translated 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...
متن کاملStep Size in Stein's Method of Exchangeable Pairs
Stein’s method of exchangeable pairs is examined through five examples in relation to Poisson and normal distribution approximation. In particular, in the case where the exchangeable pair is constructed from a reversible Markov chain, we analyze how modifying the step size of the chain in a natural way affects the error term in the approximation acquired through Stein’s method. It has been note...
متن کامل1. Use of exchangeable pairs in the analysis of simulations
The method of exchangeable pairs has emerged as an important tool in proving limit theorems for Poisson, normal and other classical approximations. Here the method is used in a simulation context. We estimate transition probabilitites from the simulations and use these to reduce variances. Exchangeable pairs are used as control variates. Finally, a general approximation theorem is developed tha...
متن کاملUse of Exchangeable Pairs in the Analysis of Simulations
The method of exchangeable pairs has emerged as an important tool in proving limit theorems for Poisson, normal and other classical approximations. Here the method is used in a simulation context. We estimate transition probabilitites from the simulations and use these to reduce variances. Exchangeable pairs are used as control variates. Finally, a general approximation theorem is developed tha...
متن کاملRandom Subgraph Countsand U -statistics: Multivariate Normal Approximation via Exchangeable Pairs and Embedding
In Reinert and Röllin (2009) a new approach—called the ‘embedding method’—was introduced, which allows us tomake use of exchangeable pairs for normal andmultivariate normal approximations with Stein’s method in cases where the corresponding couplings do not satisfy a certain linearity condition. The key idea is to embed the problem into a higher-dimensional space in such a way that the linearit...
متن کامل