Mathew D. Penrose
Multivariate normal approximation in geometric probability
Penrose, Mathew D.; Wade, Andrew R.
Abstract
Consider a measure = Px xx where the sum is over points x of a Poisson point process of intensity on a bounded region in d-space, and x is a functional determined by the Poisson points near to x, i.e. satisfying an exponential stabilization condition, along with a moments condition (examples include statistics for proximity graphs, germ-grain models and random sequential deposition models). A known general result says the - measures (suitably scaled and centred) of disjoint sets in Rd are asymptotically independent normals as ! 1; here we give an O(
Citation
Penrose, M. D., & Wade, A. R. (2008). Multivariate normal approximation in geometric probability. Journal of statistical theory and practice, 2(2), 293-326. https://doi.org/10.1080/15598608.2008.10411876
Journal Article Type | Article |
---|---|
Publication Date | Jun 1, 2008 |
Deposit Date | Oct 4, 2012 |
Publicly Available Date | Jan 31, 2013 |
Journal | Journal of Statistical Theory and Practice |
Electronic ISSN | 1559-8616 |
Publisher | Springer |
Peer Reviewed | Peer Reviewed |
Volume | 2 |
Issue | 2 |
Pages | 293-326 |
DOI | https://doi.org/10.1080/15598608.2008.10411876 |
Keywords | Multivariate normal approximation, Geometric probability, Stabilization, Central limit theorem, Stein's method, Nearest-neighbour graph. |
Public URL | https://durham-repository.worktribe.com/output/1495625 |
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Copyright Statement
This is an electronic version of an article published in Penrose, Mathew D. and Wade, Andrew R. (2008) 'Multivariate normal approximation in geometric probability.', Journal of statistical theory and practice., 2 (2). pp. 293-326. Journal of statistical theory and practice is available online at: http://www.tandfonline.com/openurl?genre=article&issn=1559-8608&volume=2&issue2&spage=293
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