2005/03/25 by Tailen Hsing, Holger Rootzen
Mathematics · #math.PR #msc:60D05 #msc:60F05
paper · pdf · doi:10.1214/009117904000001008
published as Annals of Probability 2005, Vol. 33, No. 1, 413-444 · Published at http://dx.doi.org/10.1214/009117904000001008 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
arxiv created 2005/03/25 · arxiv updated 2009/12/01
This paper considers the asymptotic distribution of the longest edge of the minimal spanning tree and nearest neighbor graph on X1,...,XNn where X1,X2,... are i.i.d. in \Re2 with distribution F and Nn is independent of the Xi and satisfies Nn/n→p1. A new approach based on spatial blocking and a locally orthogonal coordinate system is developed to treat cases for which F has unbounded support. The general results are applied to a number of special cases, including elliptically contoured distributions, distributions with independent Weibull-like margins and distributions with parallel level curves.