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Abstract:
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We represent the observations of a random sample as vertices of a complete weighted graph and propose new depth functions that are applicable to multivariate distributions and data on graphs. We define and compare several depth functions on the minimal spanning tree (MST), including Path, Eccentricity, Peeling, Runt, and Geodesic Convexity depth functions, classify them into four types and study their properties. We consider the corresponding multidimensional medians, investigate their robustness, computational complexity and compare them in a simulation study to find the median vertex under different distributions and sample sizes. An example illustrates the use of the MST-based depth functions.
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