Upper bounds for stein-type operators

Electronic Journal of Probability

Volumn 13, Issue , 2008, Pages 566-587

  Daly, Fraser ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

Central limit theorem; Poisson Charlier approximation; Stein type operator; Stein s method; Stochastic ordering

Indexed keywords

EID: 42449110025     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v13-479     Document Type: Article

References (25)

1. A. D. Barbour, Asymptotic expansions based on smooth functions in the central limit theorem, Probab. Theory Relat. Fields 72 (1986), no. 2, 289-303.
2. A. D. Barbour, Asymptotic expansions in the Poisson limit theorem, Ann. Probab. 15 (1987), no. 2, 748-766.
3. A. D. Barbour, Stein's method for diffusion approximations, Probab. Theory Related Fields 84 (1990), no. 3, 297-322.
4. A. D. Barbour, L. Holst and S. Janson, Poisson approximation, Oxford Univ. Press, New York, 1992.
5. A. D. Barbour and A. Xia, On Stein's factors for Poisson approximation in Wasserstein distance, Bernoulli 12 (2006), no. 6, 943-954.
6. E. Bolthausen, An estimate of the remainder in a combinatorial central limit theorem, Z. Wahrsch. Verw. Gebiete 66 (1984), no. 3, 379-386.
7. T. C. Brown and A. Xia, Stein's method and birth-death processes, Ann. Probab. 29 (2001), no. 3, 1373-1403.
8. L. H. Y. Chen, Poisson approximation for dependent trials, Ann. Probability 3 (1975), no. 3, 534-545.
9. L. H. Y. Chen and Q.-M. Shao, Stein's method for normal approximation, in An introduction to Stein's method, 1-59, Singapore Univ. Press, Singapore, 2005.
10. T. Erhardsson, Stein's method for Poisson and compound Poisson approximation, in An introduction to Stein's method, 61-113, Singapore Univ. Press, Singapore, 2005.
11. L. Goldstein and G. Reinert, Stein's method and the zero bias transformation with application to simple random sampling, Ann. Appl. Probab. 7 (1997), no. 4, 935-952.
12. F. Götze, On the rate of convergence in the multivariate CLT, Ann. Probab. 19 (1991), no. 2, 724-739.
13. S. T. Ho and L. H. Y. Chen, An Lp bound for the remainder in a combinatorial central limit theorem, Ann. Probability 6 (1978), no. 2, 231-249.
14. W. Hoeffding, The extrema of the expected value of a function of independent random variables, Ann. Math. Statist. 26 (1955), 268-275.
15. S. Holmes, Stein's method for birth and death chains, in Stein's method: expository lectures and applications, 45-67, Inst. Math. Statist., Beachwood, OH, 2004.
16. C. Lefèvre and S. Utev, Exact norms of a Stein-type operator and associated stochastic orderings, Probab. Theory Related Fields 127 (2003), no. 3, 353-366.
17. E. A. Pekoz, Stein's method for geometric approximation, J. Appl. Probab. 33 (1996), no. 3, 707-713.
18. M. J. Phillips and G. V. Weinberg, Non-uniform bounds for geometric approximation, Statist. Probab. Lett. 49 (2000), no. 3, 305-311.
19. G. Reinert, A weak law of large numbers for empirical measures via Stein's method, Ann. Probab. 23 (1995), no. 1, 334-354.
20. G. Reinert, Three general approaches to Stein's method, in An introduction to Stein's method, 183-221, Singapore Univ. Press, Singapore, 2005.
21. Y. Rinott and V. Rotar, On Edgeworth expansions for dependency-neighborhoods chain structures and Stein's method, Probab. Theory Related Fields 126 (2003), no. 4, 528-570.
22. V. Rotar, Stein's method, Edgeworth's expansions and a formula of Barbour, in Stein's method and applications, 59-84, Singapore Univ. Press, Singapore, 2005.
23. C. Stein, A bound for the error in the normal approximation to the distribution of a sum of dependent random variables, in Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. II: Probability theory, 583-602, Univ. California Press, Berkeley, Calif, 1972.
24. C. Stein, Approximate computation of expectations, Inst. Math. Statist., Hayward, CA, 1986.
25. A. Xia, Stein's method and Poisson process approximation, in An introduction to Stein's method, 115-181, Singapore Univ. Press, Singapore, 2005.