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
487-492
Caroni, C.
6fcc8200-11ae-496e-90ed-ed1fcf1ca147
Prescott, P.
cf0adfdd-989b-4f15-9e60-ef85eed817b2
2002
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), .
(doi:10.1006/jmva.2001.2064).
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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Published date: 2002
Keywords:
asymptotic distribution, extreme values, gap test, multivariate normal, minimal spanning tree, outliers, order statistics, uniform distribution
Organisations:
Statistics
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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 Mar 2024 07:36
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Author:
C. Caroni
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