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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/19059
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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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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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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13.13397 |