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A mathematical model for variable selection in functional regression modelswith scalar response is proposed. By "variable selection" we mean a procedureto replace the whole trajectories of the functional explanatory variables withtheir values at a finite number of carefully selected instants (or "impactpoints"). The basic idea of our approach is to use the Reproducing KernelHilbert Space (RKHS) associated with the underlying process, instead of themore usual L2[0,1] space, in the definition of the linear model. This turns outto be especially suitable for variable selection purposes, since thefinite-dimensional linear model based on the selected "impact points" can beseen as a particular case of the RKHS-based linear functional model. In thisframework, we address the consistent estimation of the optimal design of impactpoints and we check, via simulations and real data examples, the performance ofthe proposed method.

An RKHS model for variable selection in functional regression