Translated poisson approximation using exchangeable pair couplings

Annals of Applied Probability

Volumn 17, Issue 5-6, 2007, Pages 1596-1614

  Röllin, Adrian ^a  

^a UNIVERSITY OF ZURICH   (Switzerland)

Author keywords

Exchangeable pairs; Local limit theorems; Stein's method; Translated Poisson distribution

Indexed keywords

EID: 49649109655     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/105051607000000258     Document Type: Article

References (17)

1. BARBOUR, A. D. and HALL, P. (1984). On the rate of Poisson convergence. Math. Proc. Cambridge Philos. Soc. 95 473-480. MR0755837
2. BARBOUR, A. D., HOLST, L. and JANSON, S. (1992). Poisson Approximation. Clarendon Press, New York. MR1163825
3. BARBOUR, A. D. and LINDVALL, T. (2006). Translated Poisson approximation for Markov chains. J. Theoret. Probab. 19 609-630. MR2280512
4. BARBOUR, A. D. and XIA, A. (1999). Poisson perturbations. ESAIM Probab. Statist. 3 131-150. MR1716120
5. CACOULLOS, T. and PAPATHANASIOU, V. (1997). Characterizations of distributions by generalizations of variance bounds and simple proofs of the CLT. J. Statist. Plann. Inference 63 157-171. MR1491576
6. CACOULLOS, T., PAPATHANASIOU, V. and UTEV, S. A. (1994). Variational inequalities with examples and an application to the central limit theorem. Ann. Probab. 22 1607-1618. MR1303658
7. ČEKANAVIČIUS, V. and Vaitkus, P. (2001). Centered Poisson approximation by the Stein method. Lithuanian Math. J. 41 319-329. MR1903485
8. CHATTERJEE, S., DIACONIS, P. and MECKES, E. (2005). Exchangeable pairs and Poisson approximation. Probab. Surv. 2 64-106. MR2121796
9. GOLDSTEIN, L. and REINERT, G. (1997). Stein's method and the zero bias transformation with application to simple random sampling. Ann. Appl. Probab. 7 935-952. MR1484792
10. GOLDSTEIN, L. and REINERT, G. (2005). Zero biasing in one and higher dimensions, and applications. In Stein's Method and Applicationsq 1-18. Singapore Univ. Press. MR2201883
11. GOLDSTEIN, L. and REINERT, G. (2005). Distributional transformations, orthogonal polynomials, and Stein characterizations. J. Theoret. Probab. 18 237-260. MR2132278
12. GOLDSTEIN, L. and XIA, A. (2006). Zero biasing and a discrete central limit theorem Ann. Probab. 34 1782-1806. MR2271482
13. HUBER, M. and REINERT, G. (2004). The stationary distribution in the antivoter model: Exact sampling and approximations. In Stein's Method: Expository Lectures and Applications 79-93. IMS, Beachwood, OH. MR2118604
14. RINOTT, Y. and ROTAR, V. (1997). On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted U-statistics. Ann. Appl. Probab. 7 1080-1105. MR1484798
15. RÖLLIN, A. (2005). Approximation of sums of conditionally independent variables by the translated Poisson distribution. Bernoulli 11 1115-1128. MR2189083
16. RÖLLIN, A. (2006, submitted manuscript). Symmetric binomial approximation for sums of locally dependent random variables. Available at www.arxiv.org/math.PR/0608138.
17. STEIN, C. (1986). Approximate Computation of Expectations. IMS, Hayward, CA. MR0882007