  In the context of high-dimensional Gaussian linear regression for ordered
variables, we study the variable selection procedure via the minimization of
the penalized least-squares criterion. We focus on model selection where the
penalty function depends on an unknown multiplicative constant commonly
calibrated for prediction. We propose a new proper calibration of this
hyperparameter to simultaneously control predictive risk and false discovery
rate. We obtain non-asymptotic bounds on the False Discovery Rate with respect
to the hyperparameter and we provide an algorithm to calibrate it. This
algorithm is based on quantities that can typically be observed in real data
applications. The algorithm is validated in an extensive simulation study and
is compared with several existing variable selection procedures. Finally, we
study an extension of our approach to the case in which an ordering of the
variables is not available.
