Which depth to use to construct functional boxplots?
Methodology
2024-09-30 v1 Applications
Abstract
This paper answers the question of which functional depth to use to construct a boxplot for functional data. It shows that integrated depths, e.g., the popular modified band depth, do not result in well-defined boxplots. Instead, we argue that infimal depths are the only functional depths that provide a valid construction of a functional boxplot. We also show that the properties of the boxplot are completely determined by properties of the one-dimensional depth function used in defining the infimal depth for functional data. Our claims are supported by (i) a motivating example, (ii) theoretical results concerning the properties of the boxplot, and (iii) a simulation study.
Cite
@article{arxiv.2409.18603,
title = {Which depth to use to construct functional boxplots?},
author = {Stanislav Nagy and Tomáš Mrkvička and Antonio Elías},
journal= {arXiv preprint arXiv:2409.18603},
year = {2024}
}