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Inapplicability of Asymptotic Results on the Minimal Spanning Tree in Statistical Testing

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  • Caroni, C.
  • Prescott, P.

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.

Suggested Citation

  • Caroni, C. & Prescott, P., 2002. "Inapplicability of Asymptotic Results on the Minimal Spanning Tree in Statistical Testing," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 487-492, November.
    • Handle: RePEc:eee:jmvana:v:83:y:2002:i:2:p:487-492
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    References listed on IDEAS

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    1. Caroni, C. & Prescott, P., 1995. "On Rohlf's Method for the Detection of Outliers in Multivariate Data," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 295-307, February.
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