Which depth to use to construct functional boxplots?

Authors

Affiliations

Antonio Elías

Universidad de Málaga, Málaga, Spain

Stanislav Nagy

Charles University, Prague, Czech Republic

Tomàs Mrkvicka

University of South Bohemia, Ceske Budejovice, Czech Republic

Important links

• Preprint

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.