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dc.contributor.authorCuesta Albertos, Juan A.
dc.contributor.authorGarcía Portugués, Eduardo
dc.contributor.authorFebrero Bande, Manuel
dc.contributor.authorGonzález Manteiga, Wenceslao
dc.identifier.citationCuesta-Albertos, Juan A.; García-Portugués, Eduardo; Febrero-Bande, Manuel; González-Manteiga, Wenceslao. Goodness-of-fit tests for the functional linear model based on randomly projected empirical processes. Ann. Statist. 47 (2019), no. 1, 439--467. doi:10.1214/18-AOS1693
dc.description.abstractWe 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.sponsorshipSupported by projects MTM2014-56235-C2-2-P and MTM2017-86061-C2-2-P from the Spanish Ministry of Economy, Industry and Competitiveness, 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 Dirección Xeral de I + D, Xunta de Galicia; IAP network StUDyS from Belgian Science Policy and in part by FPU Grant AP2010-0957 from the Spanish Ministry of Education and the Dynamical Systems Interdisciplinary Network, University of Copenhagen
dc.publisherInstitute of Mathematical Statistics
dc.relationinfo:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2016-76969-P/ES
dc.rights© Institute of Mathematical Statistics, 2019
dc.subjectEmpirical process
dc.subjectFunctional data
dc.subjectFunctional linear model
dc.subjectFunctional principal components
dc.subjectRandom projections
dc.titleGoodness-of-fit tests for the functional linear model based on randomly projected empirical processes
dc.contributor.affiliationUniversidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización

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