When predicting scalar responses in the situation where the explanatory variables are functions, it is sometimes the case that some functional variables are related to responses linearly while other variables have more complicated relationships with the responses. In this paper, we propose a new semi-parametric model to take advantage of both parametric and nonparametric functional modeling. As...

Theoretical results in the functional linear regression literature have so far focused on minimax estimation where smoothness parameters are assumed to be known and the estimators typically depend on these smoothness parameters. In this paper we consider adaptive estimation in functional linear regression. The goal is to construct a single data-driven procedure that achieves optimality results ...