Título:
Level set and density estimation on manifolds
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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:
Mathematics - Statistics theory
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Año de publicación:
2021
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Resumen:
We tackle the problem of the estimation of the level sets Lf (λ) of the density f of a random vector X supported on a smooth manifold M ⊂ Rd, from an iid sample of X. To do that we introduce a kernel-based estimator ˆfn,h, which is a slightly modified version of the one proposed in [45], and proves its a.s. uniform convergence to f . Then, we propose two estimators of Lf (λ), the first one is a plug-in: L ˆfn,h (λ), which is proven to be a.s. consistent in Hausdorff distance and distance in measure, if Lf (λ) does not meet the boundary of M . While the second one assumes that Lf (λ) is r-convex, and is estimated by means of the r-convex hull of L ˆfn,h (λ). The performance of our proposal is illustrated through some simulated examples. In a real data example we analyze the intensity and direction of strong and moderate winds.
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Publicado también en: Journal of Multivariate Analysis, 2022, 189: 104925. DOI: 10.1016/j.jmva.2021.104925
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EN:
Mathematics (Statistics Theory), arXiv:2003.05814, Mar 2021
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ANII: FCE_1_2019_1_156054
Citación:
Cholaquidis, A, Fraiman, R y Moreno, L. "Level set and density estimation on manifolds". [Preprint]. Publicado en: Mathematics (Statistics Theory). 2021, arXiv:2003.05814, Mar 2021. 26 h.
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Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| 2003.05814.pdf | Preprint | 2.14 MB | Adobe PDF |