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Campo DC | Valor | Lengua/Idioma |
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dc.contributor.author | Cholaquidis, Alejandro | - |
dc.contributor.author | Cuevas, Antonio | - |
dc.date.accessioned | 2023-06-02T14:25:26Z | - |
dc.date.available | 2023-06-02T14:25:26Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | Cholaquidis, A y Cuevas, A. "On estimation of biconvex sets". [Preprint] Publicado en: Mathematics (Statistics Theory). 2020, arXiv:1810.08057, Jun 2020. 27 h. | es |
dc.identifier.uri | https://hdl.handle.net/20.500.12008/37372 | - |
dc.description | Publicado también en: ESAIM: Probability and Statistics, 2020, 24: 770-788. DOI: 10.1051/ps/2020019 | es |
dc.description.abstract | A set in the Euclidean plane is said to be biconvex if, for some angle θ ∈ [0, π/2), all its sections along straight lines with inclination angles θ and θ+π/2 are convex sets (i.e, empty sets or segments). Biconvexity is a natural notion with some useful applications in optimization theory. It has also be independently used, under the name of “rectilinear convexity”, in computational geometry. We are concerned here with the problem of asymptotically reconstructing (or estimating) a biconvex set S from a random sample of points drawn on S. By analogy with the classical convex case, one would like to define the “biconvex hull” of the sample points as a natural estimator for S. However, as previously pointed out by several authors, the notion of “hull” for a given set A (understood as the “minimal” set including A and having the required property) has no obvious, useful translation to the biconvex case. This is in sharp contrast with the well-known elementary definition of convex hull. Thus, we have selected the most commonly accepted notion of “biconvex hull” (often called “rectilinear convex hull”): we first provide additional motivations for this definition, proving some useful relations with other convexity-related notions. Then, we prove some results concerning the consistent approximation of a biconvex set S and and the corresponding biconvex hull. An analogous result is also provided for the boundaries. A method to approximate, from a sample of points on S, the biconvexity angle θ is also given. | es |
dc.description.sponsorship | ANII: FCE_1_2019_1_156054 | es |
dc.format.extent | 27 h | es |
dc.format.mimetype | application/pdf | es |
dc.language.iso | en | es |
dc.publisher | arXiv | es |
dc.relation.ispartof | Mathematics (Statistics Theory), arXiv:1810.08057, Jun 2020 | es |
dc.rights | Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014) | es |
dc.subject | Set estimation | es |
dc.subject | Biconvex sets, biconvex hull | es |
dc.subject | Hausdorff metric | es |
dc.title | On estimation of biconvex sets | es |
dc.type | Preprint | es |
dc.contributor.filiacion | Cholaquidis Alejandro, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. | - |
dc.contributor.filiacion | Cuevas Antonio, Universidad Autónoma de Madrid | - |
dc.rights.licence | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) | es |
dc.identifier.doi | 10.48550/arXiv.1810.08057 | - |
Aparece en las colecciones: | Publicaciones académicas y científicas - Facultad de Ciencias |
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1810.08057.pdf | Preprint | 741,98 kB | Adobe PDF | Visualizar/Abrir |
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