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