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Multivariate normal approximation in geometric probability.

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.

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(

Item Type:Article
Keywords:Multivariate normal approximation, Geometric probability, Stabilization, Central limit theorem, Stein's method, Nearest-neighbour graph.
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1080/15598608.2008.10411876
Publisher 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
Date accepted:No date available
Date deposited:31 January 2013
Date of first online publication:June 2008
Date first made open access:No date available

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