B0756
Title: Locally sparse function-on-function regression
Authors: Marco Stefanucci - University of Rome Tor Vergata (Italy) [presenting]
Antonio Canale - University of Padua (Italy)
Mauro Bernardi - University of Padova (Italy)
Abstract: The focus is on functional linear regression, and specifically, we consider models for functional response and functional covariates. The literature proposes two approaches to address this situation: the concurrent functional model and the non-concurrent functional model. In the former, the value of the functional response at a given domain point depends only on the value of the functional regressors evaluated at the same domain point, while in the latter the functional covariates evaluated in each point of their domain have a non-null effect on the response in any point of its domain. To balance these two extremes, we propose a locally sparse functional regression model in which the functional regression coefficient is allowed -- and not forced -- to be exactly zero for a subset of its domain. We achieve this by means of a suitable basis representation of the functional regression coefficient and exploiting an overlap group-Lasso penalty for its estimation. Efficient computational strategies based on majorization-minimization algorithms are introduced, and appealing theoretical properties in terms of models support and consistency of the proposed estimator are discussed. The empirical performance of the method is illustrated through simulation studies and an application related to human mortality.
