Depth functions and mutidimensional medians on minimal spanning trees

Mengta Yang, Reza Modarres and Lingzhe Guo

Journal of Applied Statistics, 2020, vol. 47, issue 2, 323-336

Abstract: Based on the minimal spanning tree (MST) of the observed data set, the paper introduces new notions of data depth and medians for multivariate data. The MST of a data set of size n is the MST of the complete weighted undirected graph on n vertices, where the edge weights are the pairwise distances of the data points. We study several properties of the MST-based depth functions. We consider the corresponding multidimensional medians, investigate their robustness and computational complexity. An example illustrates the use of the MST-based depth functions.

Date: 2020
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DOI: 10.1080/02664763.2019.1636939

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