Normal approximation for coverage models over binomial point processes

Larry Goldstein; Mathew D. Penrose

doi:10.1214/09-aap634

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arXiv · 0812.3084

Normal approximation for coverage models over binomial point processes

Larry Goldstein·Mathew D. Penrose

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Abstract

We give error bounds which demonstrate optimal rates of convergence in the CLT for the total covered volume and the number of isolated shapes, for germ-grain models with fixed grain radius over a binomial point process of $n$ points in a toroidal spatial region of volume $n$. The proof is based on Stein's method via size-biased couplings.

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Larry Goldstein, Mathew D. Penrose. 2008-12-16. Normal approximation for coverage models over binomial point processes. https://doi.org/10.1214/09-aap634

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