Simultaneous confidence bands for nonparametric regression with repeated measurements data

We look into nonparametric regression with repeated measurements collected on a fine grid. An asymptotic normality result is obtained in a function space. This result can be used to build simultaneous confidence bands (SCB) for various tasks in statistical exploration, estimation and inference. Two applications are proposed: one is a SCB procedure for the regression function and the other is a goodness-of-fit test for linear regression models. The first one improves upon other available methods in terms of accuracy 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 is also provided.