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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| Format: | article |
| Language: | English |
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2024
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| Online Access: | https://hdl.handle.net/20.500.12008/48454 |
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| _version_ | 1868889954783854592 |
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| author | Berrendero, José |
| author2 | Cholaquidis, Alejandro Cuevas, Antonio |
| author2_role | author author |
| author_browse | Berrendero, José Cholaquidis, Alejandro Cuevas, Antonio |
| author_facet | Berrendero, José Cholaquidis, Alejandro Cuevas, Antonio |
| author_role | author |
| collection | COLIBRI |
| dc.contributor.none.fl_str_mv | Berrendero José Cholaquidis Alejandro, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. Cuevas Antonio |
| dc.creator.none.fl_str_mv | Berrendero, José Cholaquidis, Alejandro Cuevas, Antonio |
| dc.date.none.fl_str_mv | 2024 2025-02-17T18:23:36Z 2025-02-17T18:23:36Z |
| dc.format.none.fl_str_mv | 35 h. application/pdf |
| dc.identifier.none.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. https://hdl.handle.net/20.500.12008/48454 10.1007/s00362-024-01567-9 |
| dc.language.none.fl_str_mv | en eng |
| dc.publisher.none.fl_str_mv | Springer |
| 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 Licencia Creative Commons Atribución (CC - By 4.0) |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.none.fl_str_mv | FUNCTIONAL DATA ANALYSIS FUNCTIONAL REGRESSION RKHS METHODS COMPARISON OF LINEAR MODELS |
| dc.title.none.fl_str_mv | On the functional regression model and its finite-dimensional approximations |
| dc.type.none.fl_str_mv | Artículo info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| 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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | anni_0ef2ede49299896f5efcb1b5d4e2cafd |
| 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 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | anni |
| network_name_str | oai-lr-anni |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/48454 |
| publishDate | 2024 |
| publishDateSort | 2024 |
| publisher.none.fl_str_mv | Springer |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | Licencia Creative Commons Atribución (CC - By 4.0) |
| spelling | On the functional regression model and its finite-dimensional approximationsBerrendero, JoséCholaquidis, AlejandroCuevas, AntonioFUNCTIONAL DATA ANALYSISFUNCTIONAL REGRESSIONRKHS METHODSCOMPARISON OF LINEAR MODELSThe 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.ANII: FCE_1_2019_1_156054SpringerBerrendero JoséCholaquidis Alejandro, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Cuevas Antonio2025-02-17T18:23:36Z2025-02-17T18:23:36Z2024Artículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion35 h.application/pdfBerrendero, 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/s00362-024-01567-9reponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaenengStatistical 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)oai:colibri.udelar.edu.uy:20.500.12008/484542026-04-14T10:10:43Z |
| spellingShingle | On the functional regression model and its finite-dimensional approximations Berrendero, José FUNCTIONAL DATA ANALYSIS FUNCTIONAL REGRESSION RKHS METHODS COMPARISON OF LINEAR MODELS |
| status_str | publishedVersion |
| title | 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_short | On the functional regression model and its finite-dimensional approximations |
| title_sort | On the functional regression model and its finite-dimensional approximations |
| topic | FUNCTIONAL DATA ANALYSIS FUNCTIONAL REGRESSION RKHS METHODS COMPARISON OF LINEAR MODELS |
| url | https://hdl.handle.net/20.500.12008/48454 |