On the functional regression model and its finite-dimensional approximations

The problem of linearly predicting a scalar response Y from a functional (random) explanatory variable X = X(t), t ∈ I is considered. It is argued that the term “linearly” can be interpreted in several meaningful ways. Thus, one could interpret that (up to a random noise) Y could be expressed as a l...

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Authors: Berrendero, José, Cholaquidis, Alejandro, Cuevas, Antonio
Format: article
Status:Published version
Publication Date:2024
Country:Uruguay
Institution:Universidad de la República
Repository:COLIBRI
Language:English
OAI Identifier:oai:colibri.udelar.edu.uy:20.500.12008/48454
Online Access:https://hdl.handle.net/20.500.12008/48454
Access Level:Open access
Keyword:FUNCTIONAL DATA ANALYSIS
FUNCTIONAL REGRESSION
RKHS METHODS
COMPARISON OF LINEAR MODELS
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dc.title.none.fl_str_mv On the functional regression model and its finite-dimensional approximations
title On the functional regression model and its finite-dimensional approximations
spellingShingle On the functional regression model and its finite-dimensional approximations
Berrendero, José
FUNCTIONAL DATA ANALYSIS
FUNCTIONAL REGRESSION
RKHS METHODS
COMPARISON OF LINEAR MODELS
title_short On the functional regression model and its finite-dimensional approximations
title_full On the functional regression model and its finite-dimensional approximations
title_fullStr On the functional regression model and its finite-dimensional approximations
title_full_unstemmed On the functional regression model and its finite-dimensional approximations
title_sort On the functional regression model and its finite-dimensional approximations
dc.creator.none.fl_str_mv Berrendero, José
Cholaquidis, Alejandro
Cuevas, Antonio
author Berrendero, José
author_facet Berrendero, José
Cholaquidis, Alejandro
Cuevas, Antonio
author_role author
author2 Cholaquidis, Alejandro
Cuevas, Antonio
author2_role author
author
dc.contributor.filiacion.none.fl_str_mv Berrendero José
Cholaquidis Alejandro, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.
Cuevas Antonio
dc.subject.other.es.fl_str_mv FUNCTIONAL DATA ANALYSIS
FUNCTIONAL REGRESSION
RKHS METHODS
COMPARISON OF LINEAR MODELS
topic FUNCTIONAL DATA ANALYSIS
FUNCTIONAL REGRESSION
RKHS METHODS
COMPARISON OF LINEAR MODELS
description The problem of linearly predicting a scalar response Y from a functional (random) explanatory variable X = X(t), t ∈ I is considered. It is argued that the term “linearly” can be interpreted in several meaningful ways. Thus, one could interpret that (up to a random noise) Y could be expressed as a linear combination of a finite family of marginals X(ti ) of the process X, or a limit of a sequence of such linear combinations. This simple point of view (which has some precedents in the literature) leads to a formulation of the linear model in terms of the RKHS space generated by the covariance function of the process X(t). It turns out that such RKHS-based formulation includes the standard functional linear model, based on the inner product in the space L2[0, 1], as a particular case. It includes as well all models in which Y is assumed to be (up to an additive noise) a linear combination of a finite number of linear projections of X. Some consistency results are proved which, in particular, lead to an asymptotic approximation of the predictions derived from the general (functional) linear model in terms of finite-dimensional models based on a finite family of marginals X(ti ), for an increasing grid of points t j in I . We also include a discussion on the crucial notion of coefficient of determination (aimed at assessing the fit of the model) in this setting. A few experimental results are given.
publishDate 2024
dc.date.issued.none.fl_str_mv 2024
dc.date.accessioned.none.fl_str_mv 2025-02-17T18:23:36Z
dc.date.available.none.fl_str_mv 2025-02-17T18:23:36Z
dc.type.es.fl_str_mv Artículo
dc.type.none.fl_str_mv info:eu-repo/semantics/article
dc.type.version.none.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.citation.es.fl_str_mv Berrendero, J, Cholaquidis, A y Cuevas, A. "On the functional regression model and its finite-dimensional approximations". Statistical Papers. [en línea] 2024, 65:5167–5201. DOI: 10.1007/s00362-024-01567-9. 35 h.
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12008/48454
dc.identifier.doi.none.fl_str_mv 10.1007/s00362-024-01567-9
identifier_str_mv Berrendero, J, Cholaquidis, A y Cuevas, A. "On the functional regression model and its finite-dimensional approximations". Statistical Papers. [en línea] 2024, 65:5167–5201. DOI: 10.1007/s00362-024-01567-9. 35 h.
10.1007/s00362-024-01567-9
url https://hdl.handle.net/20.500.12008/48454
dc.language.iso.none.fl_str_mv en
eng
language_invalid_str_mv en
language eng
dc.relation.none.fl_str_mv Statistical Papers, 2024, 65:5167–5201. DOI: 10.1007/s00362-024-01567-9
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.license.none.fl_str_mv Licencia Creative Commons Atribución (CC - By 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv Licencia Creative Commons Atribución (CC - By 4.0)
dc.format.extent.es.fl_str_mv 35 h.
dc.format.mimetype.es.fl_str_mv application/pdf
dc.publisher.es.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:COLIBRI
instname:Universidad de la República
instacron:Universidad de la República
instname_str Universidad de la República
instacron_str Universidad de la República
institution Universidad de la República
reponame_str COLIBRI
collection COLIBRI
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spelling Berrendero JoséCholaquidis Alejandro, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Cuevas Antonio2025-02-17T18:23:36Z2025-02-17T18:23:36Z2024Berrendero, J, Cholaquidis, A y Cuevas, A. "On the functional regression model and its finite-dimensional approximations". Statistical Papers. [en línea] 2024, 65:5167–5201. DOI: 10.1007/s00362-024-01567-9. 35 h.https://hdl.handle.net/20.500.12008/4845410.1007/s00362-024-01567-9The problem of linearly predicting a scalar response Y from a functional (random) explanatory variable X = X(t), t ∈ I is considered. It is argued that the term “linearly” can be interpreted in several meaningful ways. Thus, one could interpret that (up to a random noise) Y could be expressed as a linear combination of a finite family of marginals X(ti ) of the process X, or a limit of a sequence of such linear combinations. This simple point of view (which has some precedents in the literature) leads to a formulation of the linear model in terms of the RKHS space generated by the covariance function of the process X(t). It turns out that such RKHS-based formulation includes the standard functional linear model, based on the inner product in the space L2[0, 1], as a particular case. It includes as well all models in which Y is assumed to be (up to an additive noise) a linear combination of a finite number of linear projections of X. Some consistency results are proved which, in particular, lead to an asymptotic approximation of the predictions derived from the general (functional) linear model in terms of finite-dimensional models based on a finite family of marginals X(ti ), for an increasing grid of points t j in I . We also include a discussion on the crucial notion of coefficient of determination (aimed at assessing the fit of the model) in this setting. A few experimental results are given.Submitted by Egaña Lachaga Florencia (florencia.egana@fic.edu.uy) on 2025-02-17T15:27:03Z No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) s00362-024-01567-9-3.pdf: 1404083 bytes, checksum: ddc9c0f268199c0f82424151539c4df8 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2025-02-17T15:31:05Z (GMT) No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) s00362-024-01567-9-3.pdf: 1404083 bytes, checksum: ddc9c0f268199c0f82424151539c4df8 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2025-02-17T18:23:36Z (GMT). No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) s00362-024-01567-9-3.pdf: 1404083 bytes, checksum: ddc9c0f268199c0f82424151539c4df8 (MD5) Previous issue date: 2024ANII: FCE_1_2019_1_15605435 h.application/pdfenengSpringerStatistical Papers, 2024, 65:5167–5201. DOI: 10.1007/s00362-024-01567-9Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución (CC - By 4.0)FUNCTIONAL DATA ANALYSISFUNCTIONAL REGRESSIONRKHS METHODSCOMPARISON OF LINEAR MODELSOn the functional regression model and its finite-dimensional approximationsArtículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaBerrendero, JoséCholaquidis, AlejandroCuevas, AntonioLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/48454/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-844http://localhost:8080/xmlui/bitstream/20.500.12008/48454/2/license_urla0ebbeafb9d2ec7cbb19d7137ebc392cMD52license_textlicense_texttext/html; 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