Influence function of projection-pursuit principal components for functional data

In the finite-dimensional setting, Li and Chen (1985) proposed a method for principal components analysis using projection-pursuit techniques. This procedure was generalized to the functional setting by Bali et al. (2011), where also different penalized estimators were defined to provide smooth func...

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Detalles Bibliográficos
Autores principales:	Bali, Juan Lucas, Boente, Graciela Lina
Publicado:	2015
Materias:	Elliptical distribution Fisher-consistency Functional principal component Influence function Robust estimation Smoothing
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0047259X_v133_n_p173_Bali http://hdl.handle.net/20.500.12110/paper_0047259X_v133_n_p173_Bali
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_0047259X_v133_n_p173_Bali
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spelling	paper:paper_0047259X_v133_n_p173_Bali2023-06-08T15:05:35Z Influence function of projection-pursuit principal components for functional data Bali, Juan Lucas Boente, Graciela Lina Elliptical distribution Fisher-consistency Functional principal component Influence function Robust estimation Smoothing In the finite-dimensional setting, Li and Chen (1985) proposed a method for principal components analysis using projection-pursuit techniques. This procedure was generalized to the functional setting by Bali et al. (2011), where also different penalized estimators were defined to provide smooth functional robust principal component estimators. This paper completes their study by deriving the influence function of the functional related to the principal direction estimators and their size. As is well known, the influence function is a measure of robustness which can also be used for diagnostic purposes. In this sense, the obtained results can be helpful for detecting influential observations for the principal directions. © 2014 Elsevier Inc. Fil:Bali, J.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Boente, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2015 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0047259X_v133_n_p173_Bali http://hdl.handle.net/20.500.12110/paper_0047259X_v133_n_p173_Bali
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Elliptical distribution Fisher-consistency Functional principal component Influence function Robust estimation Smoothing
spellingShingle	Elliptical distribution Fisher-consistency Functional principal component Influence function Robust estimation Smoothing Bali, Juan Lucas Boente, Graciela Lina Influence function of projection-pursuit principal components for functional data
topic_facet	Elliptical distribution Fisher-consistency Functional principal component Influence function Robust estimation Smoothing
description	In the finite-dimensional setting, Li and Chen (1985) proposed a method for principal components analysis using projection-pursuit techniques. This procedure was generalized to the functional setting by Bali et al. (2011), where also different penalized estimators were defined to provide smooth functional robust principal component estimators. This paper completes their study by deriving the influence function of the functional related to the principal direction estimators and their size. As is well known, the influence function is a measure of robustness which can also be used for diagnostic purposes. In this sense, the obtained results can be helpful for detecting influential observations for the principal directions. © 2014 Elsevier Inc.
author	Bali, Juan Lucas Boente, Graciela Lina
author_facet	Bali, Juan Lucas Boente, Graciela Lina
author_sort	Bali, Juan Lucas
title	Influence function of projection-pursuit principal components for functional data
title_short	Influence function of projection-pursuit principal components for functional data
title_full	Influence function of projection-pursuit principal components for functional data
title_fullStr	Influence function of projection-pursuit principal components for functional data
title_full_unstemmed	Influence function of projection-pursuit principal components for functional data
title_sort	influence function of projection-pursuit principal components for functional data
publishDate	2015
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0047259X_v133_n_p173_Bali http://hdl.handle.net/20.500.12110/paper_0047259X_v133_n_p173_Bali
work_keys_str_mv	AT balijuanlucas influencefunctionofprojectionpursuitprincipalcomponentsforfunctionaldata AT boentegracielalina influencefunctionofprojectionpursuitprincipalcomponentsforfunctionaldata
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Influence function of projection-pursuit principal components for functional data

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