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.

Article information

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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