Picture of neon light reading 'Open'

Discover open research at Strathprints as part of International Open Access Week!

23-29 October 2017 is International Open Access Week. The Strathprints institutional repository is a digital archive of Open Access research outputs, all produced by University of Strathclyde researchers.

Explore recent world leading Open Access research content this Open Access Week from across Strathclyde's many research active faculties: Engineering, Science, Humanities, Arts & Social Sciences and Strathclyde Business School.

Explore all Strathclyde Open Access research outputs...

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. 293-326. ISSN 1559-8608

[img]
Preview
PDF (strathprints013397.pdf)
strathprints013397.pdf

Download (394kB) | Preview

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 d-space, 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, germ-grain models and random sequential deposition models). A known general result says the μλ-measures (suitably scaled and centred) of disjoint sets in Rd are asymptotically independent normals as λ tends to infinity; here we give an O( λ-1/(2d + ε)) bound on the rate of convergence. We illustrate our result with an explicit multivariate central limit theorem for the nearest-neighbour graph on Poisson points on a finite collection of disjoint intervals.