Nonparametric regression on functional data: Inference and practical aspects

We consider the problem of predicting a real random variable from a functional explanatory variable. The problem is tackled using a nonparametric kernel approach, which has been recently adapted to this functional context. We derive theoretical results from a deep asymptotic analysis of the behaviour of the estimate, including mean squared convergence (with rates and precise evaluation of the constant terms) as well as asymptotic distribution. Practical use of these results relies on the ability to estimate these constants. Some perspectives in this direction are discussed. In particular, a functional version of wild bootstrapping ideas is proposed and used both on simulated and real functional datasets.