Selection of functional predictors and smooth coefficient estimation for scalar-on-function regression models
Year: 2025
Type: preprint
Abstract: In the framework of scalar-on-function regression models, in which several functional variables are employed to predict a scalar response, we propose a methodology for selecting relevant functional predictors while simultaneously providing accurate smooth (or, more generally, regular) estimates of the functional coefficients. We suppose that the functional predictors belong to a real separable Hilbert space, while the functional coefficients belong to a specific subspace of this Hilbert space. Such a subspace can be a Reproducing Kernel Hilbert Space (RKHS) to ensure the desired regularity characteristics, such as smoothness or periodicity, for the coefficient estimates. Our procedure, called SOFIA (Scalar-On-Function Integrated Adaptive Lasso), is based on an adaptive penalized least squares algorithm that leverages functional subgradients to efficiently solve the minimization problem. We demonstrate that the proposed method satisfies the functional oracle property, even when the number of predictors exceeds the sample size. SOFIA's effectiveness in variable selection and coefficient estimation is evaluated through extensive simulation studies and a real-data application to GDP growth prediction.
Source: arXiv (Cornell University)
Authors: Fathi, Hedayat, Cremona, Marzia A., Severino, Federico
Institution: Université Laval
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: Université Laval, Università degli Studi di Milano, Canadian Mathematical Society, Memorial University of Newfoundland, Università degli Studi del Piemonte Orientale, Università Bocconi, Alliance de recherche numérique du Canada, Centre interuniversitaire de recherche sur les reseaux d'entreprise, la logistique et le transport, Natural Sciences and Engineering Research Council of Canada, Social Sciences and Humanities Research Council of Canada, Fonds de Recherche du Québec - Santé
OpenAlex ID: W6948376361
Cites:
Cited by:
Related to: