Upper bounds for spatial point process approximations
Abstract
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 d_2-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.
Cite
@article{arxiv.math/0503491,
title = {Upper bounds for spatial point process approximations},
author = {Dominic Schuhmacher},
journal= {arXiv preprint arXiv:math/0503491},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.1214/105051604000000684 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)