Semi-functional partial linear regression

This note deals with the problem of predicting some real-valued response variable in the situation where some among the explanatory variables are functional. More precisely, a new model is introduced in order to capture both the advantages of a semi-linear modelling and those of the recent advances on nonparametric statistics for functional data. The aim of this note is to provide the first advances in this direction. After having constructed precisely the so-called semi-functional partially linear model, the estimates are presented and some asymptotic results (with rates of convergence) are given. Lastly, a real data example illustrates the usefulness of the model.