Statistical depth and support medians for fuzzy data
Statistics Theory
2025-05-26 v1 Statistics Theory
Abstract
Statistical depth functions order the elements of a space with respect to their centrality in a probability distribution or dataset. Since many depth functions are maximized in the real line by the median, they provide a natural approach to defining median-like location estimators for more general types of data (in our case, fuzzy data). We analyze the relationships between depth-based medians, medians based on the support function, and some notions of a median for fuzzy data in the literature. We take advantage of specific depth functions for fuzzy data defined in our former papers: adaptations of Tukey depth, simplicial depth, -depth and projection depth.
Cite
@article{arxiv.2310.13478,
title = {Statistical depth and support medians for fuzzy data},
author = {Luis González-De La Fuente and Alicia Nieto-Reyes and Pedro Terán},
journal= {arXiv preprint arXiv:2310.13478},
year = {2025}
}