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

16 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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title = "Normal approximation for coverage models over binomial point processes",

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 - Goldstein, L

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

KW - Stein's method

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DO - 10.1214/09-aap634

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SN - 1050-5164

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SP - 696

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JO - Annals of Applied Probability

JF - Annals of Applied Probability

IS - 2

ER -

Normal approximation for coverage models over binomial point processes

Abstract

Keywords

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