Symmetric and centered binomial approximation of sums of locally dependent random variables
Adrian Roellin, University of Oxford
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.
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