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January 2005 Extremes on trees
Tailen Hsing, Holger Rootzén
Ann. Probab. 33(1): 413-444 (January 2005). DOI: 10.1214/009117904000001008


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/np1. 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.


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Tailen Hsing. Holger Rootzén. "Extremes on trees." Ann. Probab. 33 (1) 413 - 444, January 2005.


Published: January 2005
First available in Project Euclid: 11 February 2005

zbMATH: 1096.60009
MathSciNet: MR2118869
Digital Object Identifier: 10.1214/009117904000001008

Primary: 60D05 , 60F05

Keywords: Extreme values , Minimal spanning tree , nearest neighbor graph

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 1 • January 2005
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