The Annals of Statistics

Multidimensional medians arising from geodesics on graphs

Christopher G. Small

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Abstract

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

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

Dates
First available: 12 September 2002

Permanent link to this document
http://projecteuclid.org/euclid.aos/1031833660

Mathematical Reviews number (MathSciNet)
MR1439310

Digital Object Identifier
doi:10.1214/aos/1031833660

Zentralblatt MATH identifier
0923.62070

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

Keywords
Median graph convex set permutation minimal spanning tree

Citation

Small, Christopher G. Multidimensional medians arising from geodesics on graphs. The Annals of Statistics 25 (1997), no. 2, 478--494. doi:10.1214/aos/1031833660. http://projecteuclid.org/euclid.aos/1031833660.


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