S-Estimators for Functional Principal Component Analysis

Autores
Boente Boente, Graciela Lina; Salibian Barrera, Matías Octavio
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Principal component analysis is a widely used technique that provides an optimal lower-dimensional approximation to multivariate or functional datasets. These approximations can be very useful in identifying potential outliers among high-dimensional or functional observations. In this article, we propose a new class of estimators for principal components based on robust scale estimators. For a fixed dimension q, we robustly estimate the q-dimensional linear space that provides the best prediction for the data, in the sense of minimizing the sum of robust scale estimators of the coordinates of the residuals. We also study an extension to the infinite-dimensional case. Our method is consistent for elliptical random vectors, and is Fisher consistent for elliptically distributed random elements on arbitrary Hilbert spaces. Numerical experiments show that our proposal is highly competitive when compared with other methods. We illustrate our approach on a real dataset, where the robust estimator discovers atypical observations that would have been missed otherwise. Supplementary materials for this article are available online.
Fil: Boente Boente, Graciela Lina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Salibian Barrera, Matías Octavio. University of British Columbia; Canadá
Materia
Functional Data Analysis
Robust Estimation
Sparse Data
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/19059

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spelling S-Estimators for Functional Principal Component AnalysisBoente Boente, Graciela LinaSalibian Barrera, Matías OctavioFunctional Data AnalysisRobust EstimationSparse Datahttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Principal component analysis is a widely used technique that provides an optimal lower-dimensional approximation to multivariate or functional datasets. These approximations can be very useful in identifying potential outliers among high-dimensional or functional observations. In this article, we propose a new class of estimators for principal components based on robust scale estimators. For a fixed dimension q, we robustly estimate the q-dimensional linear space that provides the best prediction for the data, in the sense of minimizing the sum of robust scale estimators of the coordinates of the residuals. We also study an extension to the infinite-dimensional case. Our method is consistent for elliptical random vectors, and is Fisher consistent for elliptically distributed random elements on arbitrary Hilbert spaces. Numerical experiments show that our proposal is highly competitive when compared with other methods. We illustrate our approach on a real dataset, where the robust estimator discovers atypical observations that would have been missed otherwise. Supplementary materials for this article are available online.Fil: Boente Boente, Graciela Lina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaFil: Salibian Barrera, Matías Octavio. University of British Columbia; CanadáAmerican Statistical Association2015-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19059Boente Boente, Graciela Lina; Salibian Barrera, Matías Octavio; S-Estimators for Functional Principal Component Analysis; American Statistical Association; Journal of The American Statistical Association; 110; 511; 7-2015; 1100-11110162-1459CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1080/01621459.2014.946991info:eu-repo/semantics/altIdentifier/url/http://www.tandfonline.com/doi/full/10.1080/01621459.2014.946991info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:11:31Zoai:ri.conicet.gov.ar:11336/19059instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:11:32.069CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv S-Estimators for Functional Principal Component Analysis
title S-Estimators for Functional Principal Component Analysis
spellingShingle S-Estimators for Functional Principal Component Analysis
Boente Boente, Graciela Lina
Functional Data Analysis
Robust Estimation
Sparse Data
title_short S-Estimators for Functional Principal Component Analysis
title_full S-Estimators for Functional Principal Component Analysis
title_fullStr S-Estimators for Functional Principal Component Analysis
title_full_unstemmed S-Estimators for Functional Principal Component Analysis
title_sort S-Estimators for Functional Principal Component Analysis
dc.creator.none.fl_str_mv Boente Boente, Graciela Lina
Salibian Barrera, Matías Octavio
author Boente Boente, Graciela Lina
author_facet Boente Boente, Graciela Lina
Salibian Barrera, Matías Octavio
author_role author
author2 Salibian Barrera, Matías Octavio
author2_role author
dc.subject.none.fl_str_mv Functional Data Analysis
Robust Estimation
Sparse Data
topic Functional Data Analysis
Robust Estimation
Sparse Data
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Principal component analysis is a widely used technique that provides an optimal lower-dimensional approximation to multivariate or functional datasets. These approximations can be very useful in identifying potential outliers among high-dimensional or functional observations. In this article, we propose a new class of estimators for principal components based on robust scale estimators. For a fixed dimension q, we robustly estimate the q-dimensional linear space that provides the best prediction for the data, in the sense of minimizing the sum of robust scale estimators of the coordinates of the residuals. We also study an extension to the infinite-dimensional case. Our method is consistent for elliptical random vectors, and is Fisher consistent for elliptically distributed random elements on arbitrary Hilbert spaces. Numerical experiments show that our proposal is highly competitive when compared with other methods. We illustrate our approach on a real dataset, where the robust estimator discovers atypical observations that would have been missed otherwise. Supplementary materials for this article are available online.
Fil: Boente Boente, Graciela Lina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Salibian Barrera, Matías Octavio. University of British Columbia; Canadá
description Principal component analysis is a widely used technique that provides an optimal lower-dimensional approximation to multivariate or functional datasets. These approximations can be very useful in identifying potential outliers among high-dimensional or functional observations. In this article, we propose a new class of estimators for principal components based on robust scale estimators. For a fixed dimension q, we robustly estimate the q-dimensional linear space that provides the best prediction for the data, in the sense of minimizing the sum of robust scale estimators of the coordinates of the residuals. We also study an extension to the infinite-dimensional case. Our method is consistent for elliptical random vectors, and is Fisher consistent for elliptically distributed random elements on arbitrary Hilbert spaces. Numerical experiments show that our proposal is highly competitive when compared with other methods. We illustrate our approach on a real dataset, where the robust estimator discovers atypical observations that would have been missed otherwise. Supplementary materials for this article are available online.
publishDate 2015
dc.date.none.fl_str_mv 2015-07
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/19059
Boente Boente, Graciela Lina; Salibian Barrera, Matías Octavio; S-Estimators for Functional Principal Component Analysis; American Statistical Association; Journal of The American Statistical Association; 110; 511; 7-2015; 1100-1111
0162-1459
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19059
identifier_str_mv Boente Boente, Graciela Lina; Salibian Barrera, Matías Octavio; S-Estimators for Functional Principal Component Analysis; American Statistical Association; Journal of The American Statistical Association; 110; 511; 7-2015; 1100-1111
0162-1459
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1080/01621459.2014.946991
info:eu-repo/semantics/altIdentifier/url/http://www.tandfonline.com/doi/full/10.1080/01621459.2014.946991
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Statistical Association
publisher.none.fl_str_mv American Statistical Association
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397