Extremes on Trees
Abstract
This paper considers the asymptotic distribution of the longest edge of the minimal spanning tree and nearest neighbor graph on X_1,...,X_{N_n} where X_1,X_2,... are i.i.d. in \Re^2 with distribution F and N_n is independent of the X_i and satisfies N_n/n\to_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.
Keywords
Cite
@article{arxiv.math/0503603,
title = {Extremes on Trees},
author = {Tailen Hsing and Holger Rootzen},
journal= {arXiv preprint arXiv:math/0503603},
year = {2007}
}
Comments
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)