2024/09/27 by Stanislav Nagy, Nagy, Stanislav, Tomáš Mrkvička +3
Agricultural and Biological Sciences · Mathematics · #Advanced Statistical Methods and Models #Applications (stat.AP) #FOS: Computer and information sciences #Methodology (stat.ME) #Sensory Analysis and Statistical Methods
paper · pdf · doi:10.48550/arxiv.2409.18603
openalex publication_date 2024/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.