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

Angelina Roche (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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 relevant covariate in this context, we propose an adaptation of the Lasso method. The criterion is based on classical Lasso inference under group sparsity (Yuan and Lin, 2006; Lounici et al., 2011). We give properties of the solution in our infinite-dimensional context. A sparsity-oracle inequality is shown and 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 method.

Domaines: Statistiques [math.ST]

Angelina Roche. VARIABLE SELECTION AND ESTIMATION IN MULTIVARIATE FUNCTIONAL LINEAR REGRESSION VIA THE LASSO. 2019. ⟨hal-01725351v2⟩