Título:
Level sets of depth measures in abstract spaces
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Autor:
Cholaquidis, Alejandro
Fraiman, Ricardo
Moreno, Leonardo
Fraiman, Ricardo
Moreno, Leonardo
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Tipo de documento:
Preprint
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Palabras clave:
Depth measures
Lens depth
Level sets
Metric spaces
Phylogenetic tree
Lens depth
Level sets
Metric spaces
Phylogenetic tree
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Año de publicación:
2021
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Resumen:
The lens depth of a point has been recently extended to general metric spaces, which is not the case for most depths. It is defined as the probability of being included in the intersection of two random balls centred at two random points X and Y, with the same radius d(X, Y). We study the consistency in Hausdorff and measure distance, of the level sets of the empirical lens depth, based on an iid sample on a general metric space. We also prove that the boundary of the empirical level sets are consistent estimators of their population counterparts, and analyze two real-life examples
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Publicado también en TEST (2023). DOI: 10.1007/s11749-023-00858-x
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Mathematics (Statistics Theory), arXiv:2011.11146, Mar 2021
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ANII: FCE_1_2019_1_156054
Citación:
Cholaquidis, A, Fraiman, R y Moreno, l. "Level sets of depth measures in abstract spaces". [Preprint]. Publicado en: Mathematics (Statistics Theory). 2021 arXiv:2011.11146, Mar 2021. 17 h.
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Licencia:
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| 2011.11146.pdf | Preprint | 704.65 KB | Adobe PDF |