Normal approximation for coverage models over binomial point processes

L Goldstein; Mathew D Penrose

doi:10.1214/09-aap634

Normal approximation for coverage models over binomial point processes

L Goldstein, Mathew D Penrose

Research output: Contribution to journal › Article › peer-review

7 Citations (SciVal)

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.

Original language	English
Pages (from-to)	696-721
Number of pages	26
Journal	Annals of Applied Probability
Volume	20
Issue number	2
DOIs	https://doi.org/10.1214/09-aap634
Publication status	Published - Apr 2010

Keywords

size biased coupling
Stochastic geometry
Berry-Esseen theorem
coverage process
Stein's method

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10.1214/09-aap634

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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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AU - Penrose, Mathew D

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AB - 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.

KW - size biased coupling

KW - Stochastic geometry

KW - Berry-Esseen theorem

KW - coverage process

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JO - Annals of Applied Probability

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SN - 1050-5164

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ER -

Normal approximation for coverage models over binomial point processes

Abstract

Keywords

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