Título:
Universally consistent estimation of the reach
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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:
2022
Contenido:
Resumen:
The reach of a set M⊂Rd, also known as condition number when M is a manifold, was introduced by Federer in 1959. The reach is a central concept in geometric measure theory, set estimation, manifold learning, among others areas. We introduce a universally consistent estimate of the reach, just assuming that the reach is positive. Under an additional assumption we provide rates of convergence. We also show that it is not possible to determine, based on a finite sample, if the reach of the support of a density is zero or not. We provide a small simulation study and a bias correction method for the case when M is a manifold.
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Publicado también en: Journal of Statistical Planning and Inference, 2023, 225: 110-120. DOI: 10.1016/j.jspi.2022.11.007
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EN:
Mathematics (Statistics Theory), arXiv:2110.12208, Nov 2022.
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ANII: FCE_1_2019_1_156054
Citación:
Cholaquidis, A, Fraiman, R y Moreno, L. "Universally consistent estimation of the reach". [Preprint]. Publicado en: Mathematics (Statistics Theory). 2022, arXiv:2110.12208, Nov 2022. 15 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 | ||
|---|---|---|---|---|---|
| 2110.12208.pdf | Preprint | 556.03 KB | Adobe PDF |