Nonparametric estimation of a trend based upon sampled continuous processes

Let X = {X (t), t ∈ [0, T]} be a second order random process of which n independent realizations are observed on a fixed grid of p time points. Under mild regularity assumptions on the sample paths of X, we show the asymptotic normality of suitable nonparametric estimators of the trend function μ = E X in the space C ([0, T]) as n, p → ∞ and, using Gaussian process theory, we derive approximate simultaneous confidence bands for μ. To cite this article: D. Degras, C. R. Acad. Sci. Paris, Ser. I 347 (2009).