  This paper aims to front with dimensionality reduction in regression setting
when the predictors are a mixture of functional variable and high-dimensional
vector. A flexible model, combining both sparse linear ideas together with
semiparametrics, is proposed. A wide scope of asymptotic results is provided:
this covers as well rates of convergence of the estimators as asymptotic
behaviour of the variable selection procedure. Practical issues are analysed
through finite sample simulated experiments while an application to Tecator's
data illustrates the usefulness of our methodology.
