Inapplicability of asymptotic results on the minimal spanning tree in statistical testing

[摘要] 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. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-11-01

[关键词] asymptotic distribution;extreme values;gap test;multivariate normal;minimal spanning tree;outliers;order statistics;uniform distribution