Goodness-of-fit tests for the functional linear model based on randomly projected empirical processes

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Show simple item record Cuesta Albertos, Juan A. García Portugués, Eduardo Febrero Bande, Mauel González Manteiga, Wenceslao 2022-07-04T09:27:00Z 2022-07-04T09:27:00Z 2019-02-01
dc.identifier.bibliographicCitation Cuesta-Albertos, J. A., García-Portugués, E., Febrero-Bande, M., & González-Manteiga, W. (2019). Goodness-of-fit tests for the functional linear model based on randomly projected empirical processes. The Annals of Statistics, 47(1).
dc.identifier.issn 0090-5364
dc.description.abstract We consider marked empirical processes indexed by a randomly projected functional covariate to construct goodness-of-fit tests for the functional linear model with scalar response. The test statistics are built from continuous functionals over the projected process, resulting in computationally efficient tests that exhibit root-n convergence rates and circumvent the curse of dimensionality. The weak convergence of the empirical process is obtained conditionally on a random direction, whilst the almost surely equivalence between the testing for significance expressed on the original and on the projected functional covariate is proved. The computation of the test in practice involves calibration by wild bootstrap resampling and the combination of several p-values, arising from different projections, by means of the false discovery rate method. The finite sample properties of the tests are illustrated in a simulation study for a variety of linear models, underlying processes, and alternatives. The software provided implements the tests and allows the replication of simulations and data applications.
dc.description.sponsorship Supported by projects MTM2014-56235-C2-2-P and MTM2017-86061-C2-2-P from the Spanish Ministry of Economy, Industry and Competitiveness. Supported by projects MTM2013-41383-P and MTM2016-76969-P from the Spanish Ministry of Economy, Industry and Competitiveness, and the European Regional Development Fund; project 10MDS207015PR from Direccion Xeral de I + D, Xunta de Galicia; IAP network StUDyS from Belgian Science Policy. Supported in part by FPU Grant AP2010-0957 from the Spanish Ministry of Education and the Dynamical Systems Interdisciplinary Network, University of Copenhagen.
dc.format.extent 29
dc.language.iso eng
dc.publisher Institute of Mathematical Statistics
dc.rights © 2019 Institute of Mathematical Statistics
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.subject.other Empirical process
dc.subject.other Functional data
dc.subject.other Functional linear model
dc.subject.other Functional principal components
dc.subject.other Goodness-of-fit
dc.subject.other Random projections
dc.subject.other Regression
dc.subject.other Checks
dc.subject.other Form
dc.title Goodness-of-fit tests for the functional linear model based on randomly projected empirical processes
dc.type article
dc.subject.eciencia Estadística
dc.identifier.doi 10.1214/18-AOS1693
dc.rights.accessRights openAccess
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 439
dc.identifier.publicationissue 1
dc.identifier.publicationlastpage 467
dc.identifier.publicationtitle Annals of Statistics
dc.identifier.publicationvolume 47
dc.identifier.uxxi AR/0000022827
dc.contributor.funder Ministerio de Economía, Industria y Competitividad (España)
dc.affiliation.dpto UC3M. Departamento de Estadística
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