Statistical depth in abstract metric spaces
Methodology
2021-07-30 v1
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.
Keywords
Cite
@article{arxiv.2107.13779,
title = {Statistical depth in abstract metric spaces},
author = {Gery Geenens and Alicia Nieto-Reyes and Giacomo Francisci},
journal= {arXiv preprint arXiv:2107.13779},
year = {2021}
}