Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth

We study a statistical data depth with respect to compact convex random sets, which is consistent with the multivariate Tukey depth and the Tukey depth for fuzzy sets. In addition, it provides a different perspective to the existing halfspace depth with respect to compact convex random sets. In stud...

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Detalles Bibliográficos
Autores: González de la Fuente, Luis, Nieto Reyes, Alicia|||0000-0002-0268-3322, Terán, Pedro
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/27219
Acceso en línea:https://hdl.handle.net/10902/27219
Access Level:acceso abierto
Palabra clave:Compact Convex Set
Halfspace Depth
Statistical Depth Function
Symmetry
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spelling Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey DepthGonzález de la Fuente, LuisNieto Reyes, Alicia|||0000-0002-0268-3322Terán, PedroCompact Convex SetHalfspace DepthStatistical Depth FunctionSymmetryWe study a statistical data depth with respect to compact convex random sets, which is consistent with the multivariate Tukey depth and the Tukey depth for fuzzy sets. In addition, it provides a different perspective to the existing halfspace depth with respect to compact convex random sets. In studying this depth function, we provide a series of properties for the statistical data depth with respect to compact convex random sets. These properties are an adaptation of properties that constitute the axiomatic notions of multivariate, functional, and fuzzy depth-functions and other well-known properties of depth.For L.G.-D.L.F. and A.N.-R., this research was supported by grant MTM2017-86061-C2-2-P funded by MCIN/AEI/10.13039/501100011033 and “ERDF A way of making Europe”. P.T. was supported by the Ministerio de Economía y Competitividad grant MTM2015-63971-P, the Ministerio de Ciencia, Innovación y Universidades grant PID2019-104486GB-I00, and the Consejería de Empleo, Industria y Turismo del Principado de Asturias grant GRUPIN-IDI2018-000132.MDPIUniversidad de Cantabria20222022-01-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttps://hdl.handle.net/10902/27219Mathematics, 2022, 10(15), 2758reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/272192026-06-02T12:39:31Z
dc.title.none.fl_str_mv Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth
title Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth
spellingShingle Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth
González de la Fuente, Luis
Compact Convex Set
Halfspace Depth
Statistical Depth Function
Symmetry
title_short Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth
title_full Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth
title_fullStr Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth
title_full_unstemmed Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth
title_sort Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth
dc.creator.none.fl_str_mv González de la Fuente, Luis
Nieto Reyes, Alicia|||0000-0002-0268-3322
Terán, Pedro
author González de la Fuente, Luis
author_facet González de la Fuente, Luis
Nieto Reyes, Alicia|||0000-0002-0268-3322
Terán, Pedro
author_role author
author2 Nieto Reyes, Alicia|||0000-0002-0268-3322
Terán, Pedro
author2_role author
author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Compact Convex Set
Halfspace Depth
Statistical Depth Function
Symmetry
topic Compact Convex Set
Halfspace Depth
Statistical Depth Function
Symmetry
description We study a statistical data depth with respect to compact convex random sets, which is consistent with the multivariate Tukey depth and the Tukey depth for fuzzy sets. In addition, it provides a different perspective to the existing halfspace depth with respect to compact convex random sets. In studying this depth function, we provide a series of properties for the statistical data depth with respect to compact convex random sets. These properties are an adaptation of properties that constitute the axiomatic notions of multivariate, functional, and fuzzy depth-functions and other well-known properties of depth.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10902/27219
url https://hdl.handle.net/10902/27219
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv Mathematics, 2022, 10(15), 2758
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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