Upper Bounds for Spatial Point Process Approximations
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 lar...
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| Veröffentlicht in: | The Annals of applied probability 2005-02, Vol.15 (1B), p.615-651 |
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| creator | Schuhmacher, Dominic |
| description | 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. |
| doi_str_mv | 10.1214/105051604000000684 |
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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; Project Euclid Complete |
| subjects | 60G55 62E20 62G07 Approximation Coordinate systems Density Density estimation dt₂-distance Perceptron convergence procedure Point estimators Point processes Poisson process Poisson process approximation Random variables Stein’s method Test ranges Topology total variation distance |
| title | Upper Bounds for Spatial Point Process Approximations |
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