A0231
Title: Sparse estimation of function-on-function non-concurrent linear regression models
Authors: Fabio Centofanti - Universita di Napoli Federico II (Italy) [presenting]
Matteo Fontana - Politecnico di Milano (Italy)
Antonio Lepore - Universita di Napoli Federico II (Italy)
Simone Vantini - Politecnico di Milano (Italy)
Abstract: Functional linear regression is the generalization of the classical regression analysis to the context of the functional data analysis. In particular, we focus on the function-on-function non-concurrent linear regression models (FonFLM) where both the regressor and the response variable have a functional form and where every point-wise evaluation of the response function possibly depends on every point-wise evaluation of the regressor function. No matter the sample size, FonFLMs are naturally over-parametrized and thus their estimation urges the introduction of penalization methods. We propose a new approach to the estimation of the regression operator of FonFLMs (i.e., S-LASSO) derived from the introduction in the loss function of both a LASSO like and a roughness penalization of the kernel of the regression operator that are able to annihilate the regression kernel on regions with smooth boundaries. After presenting some valuable asymptotic properties, we will then show by means of simulations that, with respect to other state-of-the-art techniques, the proposed estimator guarantees much higher interpretability, better predictive performances without any major loss in the estimation accuracy either the kernel is sparse or not.
