Lower bounds for computing statistical depth

Given a 0nite set of points S, two measures of the depth of a query point with respect to S are the Simplicial depth of Liu andthe Halfspace depth of Tukey (also known as Location depth). We show that computing these depths requires 4(n log n) time, which matches the upper boundcomplexities of the a...

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Detalhes bibliográficos
Autores: Aloupis, G., Cortés Parejo, María del Carmen, Gomez, F., Soss, M., Toussaint, G.
Tipo de documento: artigo
Estado:Versión aceptada para publicación
Data de publicação:2002
País:España
Recursos:Universidad de Sevilla (US)
Repositório:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/163675
Acesso em linha:https://hdl.handle.net/11441/163675
https://doi.org/10.1016/S0167-9473(02)00032-4
Access Level:Acceso aberto
Palavra-chave:Simplicial depth
Halfspace depth
Liu
Tukey
Sign tests
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repository_id_str
spelling Lower bounds for computing statistical depthAloupis, G.Cortés Parejo, María del CarmenGomez, F.Soss, M.Toussaint, G.Simplicial depthHalfspace depthLiuTukeySign testsGiven a 0nite set of points S, two measures of the depth of a query point with respect to S are the Simplicial depth of Liu andthe Halfspace depth of Tukey (also known as Location depth). We show that computing these depths requires 4(n log n) time, which matches the upper boundcomplexities of the algorithms of Rousseeuw andRuts. Our lower boundproofs may also be appliedto two bivariate sign tests: that of Hodges, andthat of Oja and Nyblom.ElsevierMatemática Aplicada I2002info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/163675https://doi.org/10.1016/S0167-9473(02)00032-4reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésComputational statistics & data analysis, 40 (2), 223-229.https://www.sciencedirect.com/science/article/abs/pii/S0167947302000324?via%3Dihubinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/1636752026-06-17T12:51:07Z
dc.title.none.fl_str_mv Lower bounds for computing statistical depth
title Lower bounds for computing statistical depth
spellingShingle Lower bounds for computing statistical depth
Aloupis, G.
Simplicial depth
Halfspace depth
Liu
Tukey
Sign tests
title_short Lower bounds for computing statistical depth
title_full Lower bounds for computing statistical depth
title_fullStr Lower bounds for computing statistical depth
title_full_unstemmed Lower bounds for computing statistical depth
title_sort Lower bounds for computing statistical depth
dc.creator.none.fl_str_mv Aloupis, G.
Cortés Parejo, María del Carmen
Gomez, F.
Soss, M.
Toussaint, G.
author Aloupis, G.
author_facet Aloupis, G.
Cortés Parejo, María del Carmen
Gomez, F.
Soss, M.
Toussaint, G.
author_role author
author2 Cortés Parejo, María del Carmen
Gomez, F.
Soss, M.
Toussaint, G.
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
dc.subject.none.fl_str_mv Simplicial depth
Halfspace depth
Liu
Tukey
Sign tests
topic Simplicial depth
Halfspace depth
Liu
Tukey
Sign tests
description Given a 0nite set of points S, two measures of the depth of a query point with respect to S are the Simplicial depth of Liu andthe Halfspace depth of Tukey (also known as Location depth). We show that computing these depths requires 4(n log n) time, which matches the upper boundcomplexities of the algorithms of Rousseeuw andRuts. Our lower boundproofs may also be appliedto two bivariate sign tests: that of Hodges, andthat of Oja and Nyblom.
publishDate 2002
dc.date.none.fl_str_mv 2002
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/163675
https://doi.org/10.1016/S0167-9473(02)00032-4
url https://hdl.handle.net/11441/163675
https://doi.org/10.1016/S0167-9473(02)00032-4
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Computational statistics & data analysis, 40 (2), 223-229.
https://www.sciencedirect.com/science/article/abs/pii/S0167947302000324?via%3Dihub
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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