Out-of-sample prediction in multidimensional P-spline models

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dc.contributor.author Carballo González, Alba
dc.contributor.author Durbán Reguera, María Luz
dc.contributor.author Lee, Dae-Jin
dc.date.accessioned 2022-03-17T10:04:58Z
dc.date.available 2022-03-17T10:04:58Z
dc.date.issued 2021-08-01
dc.identifier.bibliographicCitation Carballo, A., Durbán, M., & Lee, D.-J. (2021). Out-of-Sample Prediction in Multidimensional P-Spline Models. In Mathematics (Vol. 9, Issue 15, p. 1761). MDPI AG.
dc.identifier.issn 2227-7390
dc.identifier.uri http://hdl.handle.net/10016/34404
dc.description.abstract The prediction of out-of-sample values is an interesting problem in any regression model. In the context of penalized smoothing using a mixed-model reparameterization, a general framework has been proposed for predicting in additive models but without interaction terms. The aim of this paper is to generalize this work, extending the methodology proposed in the multidimensional case, to models that include interaction terms, i.e., when prediction is carried out in a multidimensional setting. Our method fits the data, predicts new observations at the same time, and uses constraints to ensure a consistent fit or impose further restrictions on predictions. We have also developed this method for the so-called smooth-ANOVA model, which allows us to include interaction terms that can be decomposed into the sum of several smooth functions. We also develop this methodology for the so-called smooth-ANOVA models, which allow us to include interaction terms that can be decomposed as a sum of several smooth functions. To illustrate the method, two real data sets were used, one for predicting the mortality of the U.S. population in a logarithmic scale, and the other for predicting the aboveground biomass of Populus trees as a smooth function of height and diameter. We examine the performance of interaction and the smooth-ANOVA model through simulation studies.
dc.description.sponsorship This research was funded in part by Ministerio de Ciencia e Innovación grant numbers PID2019-104901RB-I00. The third author gratefully acknowledges support by the Department of Education, Language Policy and Culture from the Basque Government (BERC 2018-2021 program), the Spanish Ministry of Economy and Competitiveness MINECO and FEDER: PID2020- 115882RB-I00/AEI/10.13039/501100011033 funded by Agencia Estatal de Investigación and acronym “S3M1P4R”, and BCAM Severo Ochoa excellence accreditation SEV-2017-0718).
dc.format.extent 23
dc.language.iso eng
dc.publisher MDPI AG
dc.rights © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
dc.rights Atribución 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by/3.0/es/
dc.subject.other Mixed models
dc.subject.other P-splines
dc.subject.other Penalized regression
dc.subject.other Prediction
dc.title Out-of-sample prediction in multidimensional P-spline models
dc.type article
dc.subject.eciencia Estadística
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.3390/math9151761
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. PID2019-104901RB-I00
dc.relation.projectID Gobierno de España. PID2020- 115882RB-I00/AEI/10.13039/501100011033
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 1761
dc.identifier.publicationissue 15
dc.identifier.publicationlastpage 1784
dc.identifier.publicationtitle Mathematics
dc.identifier.publicationvolume 9
dc.identifier.uxxi AR/0000028932
dc.contributor.funder Ministerio de Economía y Competitividad (España)
dc.contributor.funder Ministerio de Educación, Cultura y Deporte (España)
dc.contributor.funder Agencia Estatal de Investigación (España)
dc.affiliation.dpto UC3M. Departamento de Estadística
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