Normal approximation for coverage models over binomial point processes
نویسندگان
چکیده
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. 1 Department of Mathematics, University of Southern California, Los Angeles, CA 90089-2532 USA [email protected] 2 Department of Mathematical Sciences, University of Bath, Bath BA1 7AY, United Kingdom: [email protected] 2 Partially supported by the Alexander von Humboldt Foundation through a FriedrichWilhelm Bessel Research Award.
منابع مشابه
Normal Approximation for Coverage Models over Binomial Point Processes by Larry Goldstein
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. 1. Introduction. Given a collection of n independent uniform...
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