Statistical depth in abstract metric spaces

Gery Geenens; Alicia Nieto-Reyes; Giacomo Francisci

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arXiv · 2107.13779

Statistical depth in abstract metric spaces

Gery Geenens·Alicia Nieto-Reyes·Giacomo Francisci

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Abstract

The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion a ranking of observations which is absent in more than one dimension. Motivated by the rapid development of technology, in particular the advent of `Big Data', we extend here that concept to general metric spaces, propose a natural depth measure and explore its properties as a statistical depth function. Working in a general metric space allows the depth to be tailored to the data at hand and to the ultimate goal of the analysis, a very desirable property given the polymorphic nature of modern data sets. This flexibility is thoroughly illustrated by several real data analyses.

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Gery Geenens, Alicia Nieto-Reyes, Giacomo Francisci. 2021-07-29. Statistical depth in abstract metric spaces. https://arxiv.org/abs/2107.13779

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