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Inapplicability of asymptotic results on the minimal spanning tree

Inapplicability of asymptotic results on the minimal spanning tree
Inapplicability of asymptotic results on the minimal spanning tree
Penrose has given asymptotic results for the distribution of the longest edge of the minimal spanning tree and nearest neighbour graph for sets of multivariate uniformly or normally distributed points. We investigate the applicability of these results to samples of up to 100 points, in up to 10 dimensions. We conclude that the asymptotic results provide an acceptable approximation only in the uniform case. Their inaccuracy for the multivariate normal case means that they cannot be applied to improve Rohlf's gap test for an outlier in a set of multivariate data points, which depends on the longest edge of the minimal spanning tree of the set.
asymptotic distribution, extreme values, gap test, multivariate normal, minimal spanning tree, outliers, order statistics, uniform distribution
0047-259X
487-492
Caroni, C.
6fcc8200-11ae-496e-90ed-ed1fcf1ca147
Prescott, P.
cf0adfdd-989b-4f15-9e60-ef85eed817b2
Caroni, C.
6fcc8200-11ae-496e-90ed-ed1fcf1ca147
Prescott, P.
cf0adfdd-989b-4f15-9e60-ef85eed817b2

Caroni, C. and Prescott, P. (2002) Inapplicability of asymptotic results on the minimal spanning tree. Journal of Multivariate Analysis, 83 (2), 487-492. (doi:10.1006/jmva.2001.2064).

Record type: Article

Abstract

Penrose has given asymptotic results for the distribution of the longest edge of the minimal spanning tree and nearest neighbour graph for sets of multivariate uniformly or normally distributed points. We investigate the applicability of these results to samples of up to 100 points, in up to 10 dimensions. We conclude that the asymptotic results provide an acceptable approximation only in the uniform case. Their inaccuracy for the multivariate normal case means that they cannot be applied to improve Rohlf's gap test for an outlier in a set of multivariate data points, which depends on the longest edge of the minimal spanning tree of the set.

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More information

Published date: 2002
Keywords: asymptotic distribution, extreme values, gap test, multivariate normal, minimal spanning tree, outliers, order statistics, uniform distribution
Organisations: Statistics

Identifiers

Local EPrints ID: 29994
URI: http://eprints.soton.ac.uk/id/eprint/29994
ISSN: 0047-259X
PURE UUID: 5324a964-f323-4723-a717-489b1251e6e1

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Date deposited: 10 May 2006
Last modified: 15 Jul 2019 19:07

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