Statistical Science· 2026Q1
Which Depth to Use to Construct Functional Boxplots?
- 1citations
- Q1SCImago
- 2026year
Short summary
Infimal depths, not integrated depths like modified band depth, construct valid functional boxplots with natural graphical interpretation.
AI-generated from the title and abstract; the full text is not read.
Key points
- Integrated functional depths (e.g., modified band depth) do not yield well-defined functional boxplots.
- Infimal depths provide a valid construction for functional boxplots with a natural graphical interpretation.
- Data transformations can be applied to infimal depth-based boxplots to detect a wider variety of outliers.
- The properties of the functional boxplot are determined by the underlying one-dimensional depth function.
AI-generated from the title and abstract; the full text is not read.
Abstract
This paper answers the question of which functional depth to use to construct a boxplot for functional data. It shows that integrated depths, for example, the popular modified band depth, do not result in well-defined boxplots. Instead, we argue that infimal depths provide a valid construction of a functional boxplot, and that they are the only functional depths that provide a natural graphical interpretation. Although the boxplots based on infimal depths per se cannot detect all kinds of outliers, suitable transformations of the data can be used to define an infimal depth-based functional boxplot sensitive to a wide variety of outliers. 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.
The authors' abstract, as published at the source. Statistical Science, 2026 · DOI ↗
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Field: Statistics and Probability
Statistics and ProbabilityMathematics