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 relevantThis research was
supported in part by Spanish Ministry of Education and Science grants MEC 2009/00035/001,
ECO2011-25706 and SEJ200
