Simultaneous confidence bands for nonparametric regression with functional data
(2009)cite arxiv:0908.1980Comment: Accepted at Statistica Sinica (SS-09-207).

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 allowing to build simultaneous confidence bands (SCB) for various estimation and inference tasks. Two 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 upon the 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 departures. A numerical study of the SCB procedures and an illustration with a speech data set are provided.
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