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Upper Bounds for Stein-Type Operators


 
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1. Title Title of document Upper Bounds for Stein-Type Operators
 
2. Creator Author's name, affiliation, country Fraser A Daly; University of Nottingham
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Stein-type operator; Stein's method; central limit theorem; Poisson-Charlier approximation; stochastic ordering
 
3. Subject Subject classification 60F05; 60J80; 62E17
 
4. Description Abstract We present sharp bounds on the supremum norm of $\mathcal{D}^jSh$ for $j\geq2$, where $\mathcal{D}$ is the differential operator and $S$ the Stein operator for the standard normal distribution. The same method is used to give analogous bounds for the exponential, Poisson and geometric distributions, with $\mathcal{D}$ replaced by the forward difference operator in the discrete case. We also discuss applications of these bounds to the central limit theorem, simple random sampling, Poisson-Charlier approximation and geometric approximation using stochastic orderings.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) University of Nottingham
 
7. Date (YYYY-MM-DD) 2008-04-12
 
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/479
 
10. Identifier Digital Object Identifier 10.1214/EJP.v13-479
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 13
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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