%0 Journal Article %1 degras2009simultaneous %A Degras, David A. %D 2009 %K non-parametric readings regression uncertainty %T Simultaneous confidence bands for nonparametric regression with functional data %U http://arxiv.org/abs/0908.1980 %X 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.

@article{degras2009simultaneous, 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 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.}, added-at = {2019-11-04T11:26:14.000+0100}, author = {Degras, David A.}, biburl = {https://www.bibsonomy.org/bibtex/26fa1777606a0dbfb05649fe1738994b9/kirk86}, description = {[0908.1980] Simultaneous confidence bands for nonparametric regression with functional data}, interhash = {62dcafd9f388d2b8df5253e49206f6ca}, intrahash = {6fa1777606a0dbfb05649fe1738994b9}, keywords = {non-parametric readings regression uncertainty}, note = {cite arxiv:0908.1980Comment: Accepted at Statistica Sinica (SS-09-207)}, timestamp = {2019-11-04T11:31:36.000+0100}, title = {Simultaneous confidence bands for nonparametric regression with functional data}, url = {http://arxiv.org/abs/0908.1980}, year = 2009 }