Variable selection and estimation in multivariate functional linear regression via the Lasso

Roche, Angelina

Roche, Angelina (2018), Variable selection and estimation in multivariate functional linear regression via the Lasso. https://basepub.dauphine.fr/handle/123456789/17935

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Type

Document de travail / Working paper

Date

2018

Titre de la collection

Cahier de recherche CEREMADE, Université Paris-Dauphine

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Auteur(s)

Roche, Angelina
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

Résumé (EN)

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.