Extremes on Trees
Journal article, 2005

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 ℜ2 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.

minimal spanning tree

Extreme values

nearest neighbor graph


Holger Rootzen

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Tailen Hsing

Annals of Probability

0091-1798 (ISSN)

Vol. 33 1 413-444

Subject Categories

Computational Mathematics

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