  We propose a new variable selection procedure for a functional linear model
with multiple scalar responses and multiple functional predictors. This method
is based on basis expansions of the involved functional predictors and
coefficients that lead to a multivariate linear regression model. Then a
criterion by means of which the variable selection problem reduces to that of
estimating a suitable set is introduced. Estimation of this set is achieved by
using appropriate penalizations of estimates of this criterion, so leading to
our proposal. A simulation study that permits to investigate the effectiveness
of the proposed approach and to compare it with existing methods is given.
