Multivariate normal approximation in geometric probability
Penrose, M.D. and Wade, A.R. (2008) Multivariate normal approximation in geometric probability. Journal of Statistical Theory and Practice, 2 (2). pp. 293326. ISSN 15598608

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Abstract
Consider a measure μλ = Σx ξx δx where the sum is over points x of a Poisson point process of intensity λ on a bounded region in dspace, and ξx 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, germgrain models and random sequential deposition models). A known general result says the μλmeasures (suitably scaled and centred) of disjoint sets in Rd are asymptotically independent normals as λ tends to infinity; here we give an O( λ1/(2d + ε)) bound on the rate of convergence. We illustrate our result with an explicit multivariate central limit theorem for the nearestneighbour graph on Poisson points on a finite collection of disjoint intervals.
Item type:  Article 

ID code:  13397 
Keywords:  multivariate normal approximation, geometric probability, stabilization, central limit theorem, Stein's method, nearestneighbour graph, statistics, Probabilities. Mathematical statistics, Mathematics, Statistics and Probability 
Subjects:  Science > Mathematics > Probabilities. Mathematical statistics Science > Mathematics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Mrs Carolynne Westwood 
Date Deposited:  12 Nov 2009 14:28 
Last modified:  01 Apr 2017 00:51 
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URI:  http://strathprints.strath.ac.uk/id/eprint/13397 
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