Level sets of depth measures in abstract spaces
Resumen:
The lens depth of a point has been recently extended to general metric spaces, which is not the case for most depths. It is defined as the probability of being included in the intersection of two random balls centred at two random points X and Y, with the same radius d(X, Y). We study the consistency in Hausdorff and measure distance, of the level sets of the empirical lens depth, based on an iid sample on a general metric space. We also prove that the boundary of the empirical level sets are consistent estimators of their population counterparts, and analyze two real-life examples
| 2021 | |
| ANII: FCE_1_2019_1_156054 | |
|
Depth measures Lens depth Level sets Metric spaces Phylogenetic tree |
|
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/37373 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522795345674240 |
|---|---|
| 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 | 2023-06-02T14:25:52Z |
| dc.date.available.none.fl_str_mv | 2023-06-02T14:25:52Z |
| dc.date.issued.none.fl_str_mv | 2021 |
| dc.description.abstract.none.fl_txt_mv | The lens depth of a point has been recently extended to general metric spaces, which is not the case for most depths. It is defined as the probability of being included in the intersection of two random balls centred at two random points X and Y, with the same radius d(X, Y). We study the consistency in Hausdorff and measure distance, of the level sets of the empirical lens depth, based on an iid sample on a general metric space. We also prove that the boundary of the empirical level sets are consistent estimators of their population counterparts, and analyze two real-life examples |
| dc.description.es.fl_txt_mv | Publicado también en TEST (2023). DOI: 10.1007/s11749-023-00858-x |
| dc.description.sponsorship.none.fl_txt_mv | ANII: FCE_1_2019_1_156054 |
| dc.format.extent.es.fl_str_mv | 17 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 sets of depth measures in abstract spaces". [Preprint]. Publicado en: Mathematics (Statistics Theory). 2021 arXiv:2011.11146, Mar 2021. 17 h. |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/37373 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.relation.ispartof.es.fl_str_mv | Mathematics (Statistics Theory), arXiv:2011.11146, 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 | Depth measures Lens depth Level sets Metric spaces Phylogenetic tree |
| dc.title.none.fl_str_mv | Level sets of depth measures in abstract spaces |
| 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/s11749-023-00858-x |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_7a83abc7efe35cbfbf1a9e4b429a9d76 |
| identifier_str_mv | Cholaquidis, A, Fraiman, R y Moreno, l. "Level sets of depth measures in abstract spaces". [Preprint]. Publicado en: Mathematics (Statistics Theory). 2021 arXiv:2011.11146, Mar 2021. 17 h. |
| 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:20.500.12008/37373 |
| 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). FCEA2023-06-02T14:25:52Z2023-06-02T14:25:52Z2021Cholaquidis, A, Fraiman, R y Moreno, l. "Level sets of depth measures in abstract spaces". [Preprint]. Publicado en: Mathematics (Statistics Theory). 2021 arXiv:2011.11146, Mar 2021. 17 h.https://hdl.handle.net/20.500.12008/37373Publicado también en TEST (2023). DOI: 10.1007/s11749-023-00858-xThe lens depth of a point has been recently extended to general metric spaces, which is not the case for most depths. It is defined as the probability of being included in the intersection of two random balls centred at two random points X and Y, with the same radius d(X, Y). We study the consistency in Hausdorff and measure distance, of the level sets of the empirical lens depth, based on an iid sample on a general metric space. We also prove that the boundary of the empirical level sets are consistent estimators of their population counterparts, and analyze two real-life examplesSubmitted by Faget Cecilia (lfaget@fcien.edu.uy) on 2023-06-02T11:31:05Z No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 2011.11146.pdf: 721561 bytes, checksum: dfabc6bc514c2601d8c9653ab418957d (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2023-06-02T13:48:04Z (GMT) No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 2011.11146.pdf: 721561 bytes, checksum: dfabc6bc514c2601d8c9653ab418957d (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2023-06-02T14:25:52Z (GMT). No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 2011.11146.pdf: 721561 bytes, checksum: dfabc6bc514c2601d8c9653ab418957d (MD5) Previous issue date: 2021ANII: FCE_1_2019_1_15605417 happlication/pdfenengMathematics (Statistics Theory), arXiv:2011.11146, 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)Depth measuresLens depthLevel setsMetric spacesPhylogenetic treeLevel sets of depth measures in abstract spacesPreprintinfo: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/20.500.12008/37373/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/37373/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | Level sets of depth measures in abstract spaces Cholaquidis, Alejandro Depth measures Lens depth Level sets Metric spaces Phylogenetic tree |
| status_str | submittedVersion |
| title | Level sets of depth measures in abstract spaces |
| title_full | Level sets of depth measures in abstract spaces |
| title_fullStr | Level sets of depth measures in abstract spaces |
| title_full_unstemmed | Level sets of depth measures in abstract spaces |
| title_short | Level sets of depth measures in abstract spaces |
| title_sort | Level sets of depth measures in abstract spaces |
| topic | Depth measures Lens depth Level sets Metric spaces Phylogenetic tree |
| url | https://hdl.handle.net/20.500.12008/37373 |
