Open Access
2023 Lasso in infinite dimension: application to variable selection in functional multivariate linear regression
Angelina Roche
Author Affiliations +
Electron. J. Statist. 17(2): 3357-3405 (2023). DOI: 10.1214/23-EJS2184


It is more and more frequently the case in applications that the data we observe come from one or more random variables taking values in an infinite dimensional space, e.g. curves. The need to have tools adapted to the nature of these data explains the growing interest in the field of functional data analysis. The model we study in this paper assumes a linear dependence between a quantity of interest and several covariates, at least one of which has an infinite dimension. To select the relevant covariates in this context, we investigate adaptations of the Lasso method. Two estimation methods are defined. The first one consists in the minimization of a Group-Lasso criterion on the multivariate functional space H. The second one minimizes the same criterion but on a finite dimensional subspaces of H whose dimension is chosen by a penalized least squares method. We prove oracle inequalities of sparsity in the case where the design is fixed or random. To compute the solutions of both criteria in practice, we propose a coordinate descent algorithm. A numerical study on simulated and real data illustrates the behavior of the estimators.

Funding Statement

The research is partly supported by the french Agence Nationale de la Recherche (ANR-18-CE40-0014 projet SMILES).


I would like to thank Vincent Rivoirard and Gaëlle Chagny for their helpful advices and careful reading of the manuscript and also the referee and associate editors whose remarks have considerably improved the quality of the article.


Download Citation

Angelina Roche. "Lasso in infinite dimension: application to variable selection in functional multivariate linear regression." Electron. J. Statist. 17 (2) 3357 - 3405, 2023.


Received: 1 March 2022; Published: 2023
First available in Project Euclid: 26 November 2023

arXiv: 1903.12414
Digital Object Identifier: 10.1214/23-EJS2184

Primary: 62G08 , 62J07
Secondary: 62J08

Keywords: Functional data analysis , Lasso , Model selection , multivariate functional linear model , projection estimators , Variable selection

Vol.17 • No. 2 • 2023
Back to Top