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Multivariate normal approximation in geometric probability

Penrose, Mathew D.; Wade, Andrew R.

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Authors

Mathew D. Penrose



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 Mar 28, 2024
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.

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