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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

Abstract

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. https://doi.org/10.1214/009117904000001008

Information

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

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

Subjects:
Primary: 60D05 , 60F05

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

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 1 • January 2005
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