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February 2005 Upper bounds for spatial point process approximations
Dominic Schuhmacher
Ann. Appl. Probab. 15(1B): 615-651 (February 2005). DOI: 10.1214/105051604000000684


We consider the behavior of spatial point processes when subjected to a class of linear transformations indexed by a variable T. It was shown in Ellis [Adv. in Appl. Probab. 18 (1986) 646–659] that, under mild assumptions, the transformed processes behave approximately like Poisson processes for large T. In this article, under very similar assumptions, explicit upper bounds are given for the d2-distance between the corresponding point process distributions. A number of related results, and applications to kernel density estimation and long range dependence testing are also presented. The main results are proved by applying a generalized Stein–Chen method to discretized versions of the point processes.


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Dominic Schuhmacher. "Upper bounds for spatial point process approximations." Ann. Appl. Probab. 15 (1B) 615 - 651, February 2005.


Published: February 2005
First available in Project Euclid: 1 February 2005

zbMATH: 1067.60022
MathSciNet: MR2114984
Digital Object Identifier: 10.1214/105051604000000684

Primary: 60G55
Secondary: 62E20 , 62G07

Keywords: Density estimation , dt₂-distance , Point processes , Poisson process approximation , Stein’s method , total variation distance

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.15 • No. 1B • February 2005
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