Lasso variable selection in functional regression

Functional Regression has been an active subject of research in the last two decades but still lacks a secure variable selection methodology. Lasso is a well known effective technique for parameters shrinkage and variable selection in regression problems. In this work we generalize the Lasso technique to select variables in the functional regression framework and show it performs well. In particular, we focus on the case of functional regression with scalar regressors and functional response. Reduce the associated functional optimization problem to a convex optimization on scalars. Find its solutions and stress their interpretability. We apply the technique to simulated data sets as well as to a new real data set: car velocity functions in low speed car accidents, a frequent cause of whiplash injuries. By “Functional Lasso” we discover which car characteristics influence more car speed and which can be considered not relevant