Indexing metadata

Distance estimates for dependent thinnings of point processes with densities


 
Dublin Core PKP Metadata Items Metadata for this Document
 
1. Title Title of document Distance estimates for dependent thinnings of point processes with densities
 
2. Creator Author's name, affiliation, country Dominic Schuhmacher; University of Western Australia, Australia
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) point process; Poisson process approximation; Stein's method; point process density; random field; thinning; total variation distance; Barbour-Brown distance
 
3. Subject Subject classification 60G55; 60E99; 60D05
 
4. Description Abstract In [Schuhmacher, Electron. J. Probab. 10 (2005), 165--201] estimates of the Barbour-Brown distance $d_2$ between the distribution of a thinned point process and the distribution of a Poisson process were derived by combining discretization with a result based on Stein's method. In the present article we concentrate on point processes that have a density with respect to a Poisson process, for which we can apply a corresponding result directly without the detour of discretization. This enables us to obtain better and more natural bounds in the $d_2$-metric, and for the first time also bounds in the stronger total variation metric. We give applications for thinning by covering with an independent Boolean model and "Matern type I" thinning of fairly general point processes. These applications give new insight into the respective models, and either generalize or improve earlier results.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2009-05-26
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/643
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-643
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
15. Rights Copyright and permissions The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.

Summary of the Creative Commons Attribution License

You are free
  • to copy, distribute, display, and perform the work
  • to make derivative works
  • to make commercial use of the work
under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.