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 equipped with the supremum norm. 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 whose accuracy improves upon other available methods, and the other is a goodness-of-fit test having the ability to detect local departures from a parametric regression shape, as opposed to the usual goodness-of-fit tests which only track global departures. A numerical study is also provided.