Which depth to use to construct functional boxplots?
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910623155093504 |
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| author | Nagy, Stanislav Mrkvička, Tomáš Elías, Antonio |
| author_facet | Nagy, Stanislav Mrkvička, Tomáš Elías, Antonio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18603 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Which depth to use to construct functional boxplots? Nagy, Stanislav Mrkvička, Tomáš Elías, Antonio Methodology Applications 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. |
| title | Which depth to use to construct functional boxplots? |
| topic | Methodology Applications |
| url | https://arxiv.org/abs/2409.18603 |