Electronic Journal of Probability

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

Adrian Roellin

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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.

Article information

Source
Electron. J. Probab., Volume 13 (2008), paper no. 24, 756-776.

Dates
Accepted: 6 May 2008
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819097

Digital Object Identifier
doi:10.1214/EJP.v13-503

Mathematical Reviews number (MathSciNet)
MR2399295

Zentralblatt MATH identifier
1189.60053

Subjects
Primary: 60F05: Central limit and other weak theorems

Keywords
Stein's method total variation metric binomial distribution local dependence

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Roellin, Adrian. Symmetric and centered binomial approximation of sums of locally dependent random variables. Electron. J. Probab. 13 (2008), paper no. 24, 756--776. doi:10.1214/EJP.v13-503. https://projecteuclid.org/euclid.ejp/1464819097


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