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

Abstract : 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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-01725351
Contributor : Angelina Roche <>
Submitted on : Thursday, September 5, 2019 - 12:02:30 PM
Last modification on : Wednesday, October 14, 2020 - 4:01:20 AM
Long-term archiving on: : Wednesday, January 8, 2020 - 11:05:24 PM

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  • HAL Id : hal-01725351, version 3
  • ARXIV : 1903.12414

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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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