The Annals of Statistics

Multidimensional medians arising from geodesics on graphs

Christopher G. Small

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In this paper we introduce a depth function for distributions on graphs that is analogous to recent multivariate definitions. Using the property of geodesic convexity on graphs, a median-like center for distributions on graphs is constructed and applied to ranking data as well as multivariate data spanned by the minimal spanning tree.

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Ann. Statist. Volume 25, Number 2 (1997), 478-494.

First available in Project Euclid: 12 September 2002

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Zentralblatt MATH identifier

Primary: 62H99: None of the above, but in this section 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Median graph convex set permutation minimal spanning tree


Small, Christopher G. Multidimensional medians arising from geodesics on graphs. Ann. Statist. 25 (1997), no. 2, 478--494. doi:10.1214/aos/1031833660.

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