VARIABLE SELECTION AND ESTIMATION IN MULTIVARIATE FUNCTIONAL LINEAR REGRESSION VIA THE LASSO - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2019

VARIABLE SELECTION AND ESTIMATION IN MULTIVARIATE FUNCTIONAL LINEAR REGRESSION VIA THE LASSO

Résumé

In more and more applications, a quantity of interest may depend on several covariates, with at least one of them infinite-dimensional (e.g. a curve). To select the relevant covariates in this context, we propose an adaptation of the Lasso method. Two estimation methods are defined. The first one consists in the minimisation of a criterion inspired by classical Lasso inference under group sparsity (Yuan and Lin, 2006; Lounici et al., 2011) on the whole multivariate functional space H. The second one minimises the same criterion but on a finite-dimensional subspace of H which dimension is chosen by a penalized leasts-squares method base on the work of Barron et al. (1999). Sparsity- oracle inequalities are proven in case of fixed or random design in our infinite-dimensional context. To calculate the solutions of both criteria, we propose a coordinate-wise descent algorithm, inspired by the glmnet algorithm (Friedman et al., 2007). A numerical study on simulated and experimental datasets illustrates the behavior of the estimators.
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Dates et versions

hal-01725351 , version 1 (07-03-2018)
hal-01725351 , version 2 (27-03-2019)
hal-01725351 , version 3 (05-09-2019)
hal-01725351 , version 4 (07-09-2021)
hal-01725351 , version 5 (01-04-2022)
hal-01725351 , version 6 (27-05-2023)

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Angelina Roche. VARIABLE SELECTION AND ESTIMATION IN MULTIVARIATE FUNCTIONAL LINEAR REGRESSION VIA THE LASSO. 2019. ⟨hal-01725351v3⟩
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