Statistical analysis of measures of non-convexity
Resumen:
Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical analysis of some of these measures of non-convexity of a set S, by dealing with their estimation based on a sample of points in S. We introduce also a new measure of non-convexity. We discuss briefly about these different notions of non-convexity, prove consistency and find the asymptotic distribution for the proposed estimators. We also consider the practical implementation of these estimators and illustrate their applicability to a real data example.
| 2022 | |
| ANII: FCE-1-2019-1-156054 | |
|
CONVEX HULL CONVEXITY MEASURE SHAPE ANALYSIS SKIN LESIONS |
|
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/44031 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522809872646144 |
|---|---|
| author | Cholaquidis, Alejandro |
| author2 | Fraiman, Ricardo Moreno, Leonardo Pateiro-López, Beatriz |
| author2_role | author author author |
| author_facet | Cholaquidis, Alejandro Fraiman, Ricardo Moreno, Leonardo Pateiro-López, Beatriz |
| 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). Facultad de Ciencias Económicas y de Administración. Pateiro-López Beatriz |
| dc.creator.none.fl_str_mv | Cholaquidis, Alejandro Fraiman, Ricardo Moreno, Leonardo Pateiro-López, Beatriz |
| dc.date.accessioned.none.fl_str_mv | 2024-06-07T16:57:40Z |
| dc.date.available.none.fl_str_mv | 2024-06-07T16:57:40Z |
| dc.date.issued.none.fl_str_mv | 2022 |
| dc.description.abstract.none.fl_txt_mv | Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical analysis of some of these measures of non-convexity of a set S, by dealing with their estimation based on a sample of points in S. We introduce also a new measure of non-convexity. We discuss briefly about these different notions of non-convexity, prove consistency and find the asymptotic distribution for the proposed estimators. We also consider the practical implementation of these estimators and illustrate their applicability to a real data example. |
| dc.description.es.fl_txt_mv | Publicado también en TEST (2023). DOI: 10.1007/s11749-023-00889-4 |
| dc.description.sponsorship.none.fl_txt_mv | ANII: FCE-1-2019-1-156054 |
| dc.format.extent.es.fl_str_mv | 32 p. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Cholaquidis, A, Fraiman, R, Moreno, L y Pateiro-López, B. "Statistical analysis of measures of non-convexity" [Preprint]. Publicado en: Mathematics (Statistics Theory). 2022, arXiv:2211.11476, nov. 2022. pp 1-32. |
| dc.identifier.doi.none.fl_str_mv | 10.48550/arXiv.2211.11476 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/44031 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | arXiv |
| dc.relation.ispartof.es.fl_str_mv | Mathematics (Statistics Theory), arXiv:2211.11476, nov. 2022 |
| 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.other.es.fl_str_mv | CONVEX HULL CONVEXITY MEASURE SHAPE ANALYSIS SKIN LESIONS |
| dc.title.none.fl_str_mv | Statistical analysis of measures of non-convexity |
| 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 TEST (2023). DOI: 10.1007/s11749-023-00889-4 |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_0f94631f4802463d1668fa3c98d8c28b |
| identifier_str_mv | Cholaquidis, A, Fraiman, R, Moreno, L y Pateiro-López, B. "Statistical analysis of measures of non-convexity" [Preprint]. Publicado en: Mathematics (Statistics Theory). 2022, arXiv:2211.11476, nov. 2022. pp 1-32. 10.48550/arXiv.2211.11476 |
| 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:20.500.12008/44031 |
| publishDate | 2022 |
| 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 MatemáticaFraiman Ricardo, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de MatemáticaMoreno Leonardo, Universidad de la República (Uruguay). Facultad de Ciencias Económicas y de Administración.Pateiro-López Beatriz2024-06-07T16:57:40Z2024-06-07T16:57:40Z2022Cholaquidis, A, Fraiman, R, Moreno, L y Pateiro-López, B. "Statistical analysis of measures of non-convexity" [Preprint]. Publicado en: Mathematics (Statistics Theory). 2022, arXiv:2211.11476, nov. 2022. pp 1-32.https://hdl.handle.net/20.500.12008/4403110.48550/arXiv.2211.11476Publicado también en TEST (2023). DOI: 10.1007/s11749-023-00889-4Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical analysis of some of these measures of non-convexity of a set S, by dealing with their estimation based on a sample of points in S. We introduce also a new measure of non-convexity. We discuss briefly about these different notions of non-convexity, prove consistency and find the asymptotic distribution for the proposed estimators. We also consider the practical implementation of these estimators and illustrate their applicability to a real data example.Submitted by Egaña Florencia (florega@gmail.com) on 2024-06-05T18:37:23Z No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 2211.11476v2.pdf: 1323063 bytes, checksum: f4f66e824af0038ea3e043ed11d4375f (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2024-06-05T18:56:33Z (GMT) No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 2211.11476v2.pdf: 1323063 bytes, checksum: f4f66e824af0038ea3e043ed11d4375f (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2024-06-07T16:57:40Z (GMT). No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 2211.11476v2.pdf: 1323063 bytes, checksum: f4f66e824af0038ea3e043ed11d4375f (MD5) Previous issue date: 2022ANII: FCE-1-2019-1-15605432 p.application/pdfenengarXivMathematics (Statistics Theory), arXiv:2211.11476, nov. 2022Las 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)CONVEX HULLCONVEXITY MEASURESHAPE ANALYSISSKIN LESIONSStatistical analysis of measures of non-convexityPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaCholaquidis, AlejandroFraiman, RicardoMoreno, LeonardoPateiro-López, BeatrizLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/44031/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/44031/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | Statistical analysis of measures of non-convexity Cholaquidis, Alejandro CONVEX HULL CONVEXITY MEASURE SHAPE ANALYSIS SKIN LESIONS |
| status_str | submittedVersion |
| title | Statistical analysis of measures of non-convexity |
| title_full | Statistical analysis of measures of non-convexity |
| title_fullStr | Statistical analysis of measures of non-convexity |
| title_full_unstemmed | Statistical analysis of measures of non-convexity |
| title_short | Statistical analysis of measures of non-convexity |
| title_sort | Statistical analysis of measures of non-convexity |
| topic | CONVEX HULL CONVEXITY MEASURE SHAPE ANALYSIS SKIN LESIONS |
| url | https://hdl.handle.net/20.500.12008/44031 |
