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Symmetric and centered binomial approximation of sums of locally dependent random variables


 
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1. Title Title of document Symmetric and centered binomial approximation of sums of locally dependent random variables
 
2. Creator Author's name, affiliation, country Adrian Roellin; University of Oxford
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Stein's method; total variation metric; binomial distribution; local dependence
 
3. Subject Subject classification 60F05
 
4. Description Abstract Stein's method is used to approximate sums of discrete and locally dependent random variables by a centered and symmetric binomial distribution, serving as a natural alternative to the normal distribution in discrete settings. The bounds are given with respect to the total variation and a local limit metric. Under appropriate smoothness properties of the summands, the same order of accuracy as in the Berry-Essen Theorem is achieved. The approximation of the total number of points of a point processes is also considered. The results are applied to the exceedances of the $r$-scans process and to the Mat'ern hardcore point process type I to obtain explicit bounds with respect to the two metrics.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Swiss National Science Foundation projects 20-107935/1 and PBZH2-117033
 
7. Date (YYYY-MM-DD) 2008-05-06
 
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/503
 
10. Identifier Digital Object Identifier 10.1214/EJP.v13-503
 
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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