Level set and density estimation on manifolds
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.
| 2021 | |
| ANII: FCE_1_2019_1_156054 | |
| Mathematics - Statistics theory | |
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/37378 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522795407540224 |
|---|---|
| author | Cholaquidis, Alejandro |
| author2 | Fraiman, Ricardo Moreno, Leonardo |
| author2_role | author author |
| author_facet | Cholaquidis, Alejandro Fraiman, Ricardo Moreno, Leonardo |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Cholaquidis Alejandro, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. Fraiman Ricardo, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. Moreno Leonardo, Universidad de la República (Uruguay). FCEA |
| dc.creator.none.fl_str_mv | Cholaquidis, Alejandro Fraiman, Ricardo Moreno, Leonardo |
| dc.date.accessioned.none.fl_str_mv | 2023-06-02T14:32:31Z |
| dc.date.available.none.fl_str_mv | 2023-06-02T14:32:31Z |
| dc.date.issued.none.fl_str_mv | 2021 |
| dc.description.abstract.none.fl_txt_mv | 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. |
| dc.description.es.fl_txt_mv | Publicado también en: Journal of Multivariate Analysis, 2022, 189: 104925. DOI: 10.1016/j.jmva.2021.104925 |
| dc.description.sponsorship.none.fl_txt_mv | ANII: FCE_1_2019_1_156054 |
| dc.format.extent.es.fl_str_mv | 26 h |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | 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. |
| dc.identifier.doi.none.fl_str_mv | 10.48550/arXiv.2003.05814 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/37378 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.relation.ispartof.es.fl_str_mv | Mathematics (Statistics Theory), arXiv:2003.05814, Mar 2021 |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.es.fl_str_mv | Mathematics - Statistics theory |
| dc.title.none.fl_str_mv | Level set and density estimation on manifolds |
| dc.type.es.fl_str_mv | Preprint |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/preprint |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/submittedVersion |
| description | Publicado también en: Journal of Multivariate Analysis, 2022, 189: 104925. DOI: 10.1016/j.jmva.2021.104925 |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_8a0a7bd81abb58852dc66f3c072d98e1 |
| identifier_str_mv | 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. 10.48550/arXiv.2003.05814 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/37378 |
| publishDate | 2021 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | mabel.seroubian@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| spelling | Cholaquidis Alejandro, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Fraiman Ricardo, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Moreno Leonardo, Universidad de la República (Uruguay). FCEA2023-06-02T14:32:31Z2023-06-02T14:32:31Z2021Cholaquidis, 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.https://hdl.handle.net/20.500.12008/3737810.48550/arXiv.2003.05814Publicado también en: Journal of Multivariate Analysis, 2022, 189: 104925. DOI: 10.1016/j.jmva.2021.104925We 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.Submitted by Faget Cecilia (lfaget@fcien.edu.uy) on 2023-06-02T12:57:25Z No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 2003.05814.pdf: 2241220 bytes, checksum: db7c1f1a95904dafd6320ba90523e06e (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2023-06-02T13:54:58Z (GMT) No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 2003.05814.pdf: 2241220 bytes, checksum: db7c1f1a95904dafd6320ba90523e06e (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2023-06-02T14:32:31Z (GMT). No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 2003.05814.pdf: 2241220 bytes, checksum: db7c1f1a95904dafd6320ba90523e06e (MD5) Previous issue date: 2021ANII: FCE_1_2019_1_15605426 happlication/pdfenengMathematics (Statistics Theory), arXiv:2003.05814, Mar 2021Las 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)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)Mathematics - Statistics theoryLevel set and density estimation on manifoldsPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaCholaquidis, AlejandroFraiman, RicardoMoreno, LeonardoLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/37378/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/37378/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; charset=utf-838782http://localhost:8080/xmlui/bitstream/20.500.12008/37378/3/license_texte8c30e04e865334cac2bfcba70aad8cbMD53license_rdflicense_rdfapplication/rdf+xml; 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- Universidad de la Repúblicafalse |
| spellingShingle | Level set and density estimation on manifolds Cholaquidis, Alejandro Mathematics - Statistics theory |
| status_str | submittedVersion |
| title | Level set and density estimation on manifolds |
| title_full | Level set and density estimation on manifolds |
| title_fullStr | Level set and density estimation on manifolds |
| title_full_unstemmed | Level set and density estimation on manifolds |
| title_short | Level set and density estimation on manifolds |
| title_sort | Level set and density estimation on manifolds |
| topic | Mathematics - Statistics theory |
| url | https://hdl.handle.net/20.500.12008/37378 |
