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A non-uniform bound for translated Poisson approximation

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1.	Title	Title of document	A non-uniform bound for translated Poisson approximation
2.	Creator	Author's name, affiliation, country	Andrew D Barbour; Universitat Zurich
2.	Creator	Author's name, affiliation, country	Kwok Pui Choi; National University of Singapore
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Stein's method; non-uniform bounds; translated Poisson approximation; total variation
3.	Subject	Subject classification	62E17; 60F05
4.	Description	Abstract	Let $X_1, \ldots , X_n$ be independent, integer valued random variables, with $p^{\text{th}}$ moments, $p >2$, and let $W$ denote their sum. We prove bounds analogous to the classical non-uniform estimates of the error in the central limit theorem, but now, for approximation of ${\cal L}(W)$ by a translated Poisson distribution. The advantage is that the error bounds, which are often of order no worse than in the classical case, measure the accuracy in terms of total variation distance. In order to have good approximation in this sense, it is necessary for ${\cal L}(W)$ to be sufficiently smooth; this requirement is incorporated into the bounds by way of a parameter $\alpha$, which measures the average overlap between ${\cal L}(X_i)$ and ${\cal L}(X_i+1), 1 \le i \le n$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2004-02-04
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/182
10.	Identifier	Digital Object Identifier	10.1214/EJP.v9-182
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 9
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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