Fast Algorithm for Impact Point Selection in Semiparametric Functional Models

Abstract

[Abstract] A new sparse semiparametric functional model is proposed, which tries to incorporate the influence of two functional variables in a scalar response in a quite simple and interpretable way. One of the functional variables is included trough a single-index structure and the other one linearly, but trough the high-dimensional vector of its discretized observations. For this model, a new algorithm for impact point selection in the linear part and for the model estimation is proposed. This procedure is based on the functional origin of the linear covariates. Some asymptotic results will ensure the good performance of the method. The computational efficiency of the algorithm, without loss of predictive power, will be showed trough a simulation study and a real data application, by comparing its results with those obtained trough the standard PLS method.