Simultaneous confidence bands for nonparametric regression with functional data

Abstract

We consider nonparametric regression in the context of functional data, that is, when a random sample of functions is observed on a fine grid. We obtain a functional asymptotic normality result that can provide simultaneous confidence bands (SCB) for various estimation and inference tasks. Applications to a SCB procedure for the regression function and to a goodness-of-fit test for curvilinear regression models are proposed. The first one has improved accuracy over other available methods, while the second can detect local departures from a parametric shape, as opposed to the usual goodness-of-fit tests which only track global depar- tures. A numerical study of the SCB procedures and an illustration with a speech data set are provided.