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

   
@article{EJP503,
	author = {Adrian Roellin},
	title = {Symmetric and centered binomial approximation of sums of locally dependent random variables},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {13},
	year = {2008},
	keywords = {Stein's method; total variation metric; binomial distribution; local dependence},
	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.},
	pages = {no. 24, 756-776},
	issn = {1083-6489},
	doi = {10.1214/EJP.v13-503},    
        url = {http://ejp.ejpecp.org/article/view/503}}