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

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dc.affiliation.dptoUC3M. Departamento de Estadísticaes
dc.contributor.authorCarballo González, Alba
dc.contributor.authorDurbán Reguera, María Luz
dc.contributor.authorLee, Dae-Jin
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.contributor.funderMinisterio de Educación, Cultura y Deporte (España)es
dc.contributor.funderAgencia Estatal de Investigación (España)es
dc.date.accessioned2022-03-17T10:04:58Z
dc.date.available2022-03-17T10:04:58Z
dc.date.issued2021-08-01
dc.description.abstractThe 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.en
dc.description.sponsorshipThis 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).en
dc.format.extent23
dc.identifier.bibliographicCitationCarballo, 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.en
dc.identifier.doihttps://doi.org/10.3390/math9151761
dc.identifier.issn2227-7390
dc.identifier.publicationfirstpage1761
dc.identifier.publicationissue15
dc.identifier.publicationlastpage1784
dc.identifier.publicationtitleMathematicsen
dc.identifier.publicationvolume9
dc.identifier.urihttps://hdl.handle.net/10016/34404
dc.identifier.uxxiAR/0000028932
dc.language.isoeng
dc.publisherMDPI AGen
dc.relation.projectIDGobierno de España. PID2019-104901RB-I00es
dc.relation.projectIDGobierno de España. PID2020- 115882RB-I00/AEI/10.13039/501100011033es
dc.rights© 2021 by the authors. Licensee MDPI, Basel, Switzerland.en
dc.rightsAtribución 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/es/*
dc.subject.ecienciaEstadísticaes
dc.subject.ecienciaMatemáticases
dc.subject.otherMixed modelsen
dc.subject.otherP-splinesen
dc.subject.otherPenalized regressionen
dc.subject.otherPredictionen
dc.titleOut-of-sample prediction in multidimensional P-spline modelsen
dc.typeresearch article*
dc.type.hasVersionVoR*
dspace.entity.typePublication
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