RT Journal Article
T1 Goodness-of-fit tests for the functional linear model based on randomly projected empirical processes
A1 Cuesta Albertos, Juan A.
A1 García Portugués, Eduardo
A1 Febrero Bande, Mauel
A1 González Manteiga, Wenceslao
AB 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.
PB Institute of Mathematical Statistics
SN 0090-5364
YR 2019
FD 2019-02-01
LK https://hdl.handle.net/10016/35386
UL https://hdl.handle.net/10016/35386
LA eng
NO 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.
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RD 1 sept. 2024