Statistical depth and support medians for fuzzy data
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912389760286720 |
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| author | La Fuente, Luis González-De Nieto-Reyes, Alicia Terán, Pedro |
| author_facet | La Fuente, Luis González-De Nieto-Reyes, Alicia Terán, Pedro |
| contents | Statistical depth functions order the elements of a space with respect to their centrality in a probability distribution or dataset. Since many depth functions are maximized in the real line by the median, they provide a natural approach to defining median-like location estimators for more general types of data (in our case, fuzzy data). We analyze the relationships between depth-based medians, medians based on the support function, and some notions of a median for fuzzy data in the literature. We take advantage of specific depth functions for fuzzy data defined in our former papers: adaptations of Tukey depth, simplicial depth, $L^1$-depth and projection depth. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_13478 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Statistical depth and support medians for fuzzy data La Fuente, Luis González-De Nieto-Reyes, Alicia Terán, Pedro Statistics Theory Statistical depth functions order the elements of a space with respect to their centrality in a probability distribution or dataset. Since many depth functions are maximized in the real line by the median, they provide a natural approach to defining median-like location estimators for more general types of data (in our case, fuzzy data). We analyze the relationships between depth-based medians, medians based on the support function, and some notions of a median for fuzzy data in the literature. We take advantage of specific depth functions for fuzzy data defined in our former papers: adaptations of Tukey depth, simplicial depth, $L^1$-depth and projection depth. |
| title | Statistical depth and support medians for fuzzy data |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2310.13478 |