Nonparametric Estimation from Correlated Copies of a Drifted Process

This paper presents several situations leading to the observation of multiple correlated copies of a drifted process, and then non-asymptotic risk bounds are established on nonparametric estimators of the drift function $b_0$ and its derivative. For drifted Gaussian processes with a regular enough covariance function, a sharper risk bound is established on the estimator of $b_0^{\mathrm{\prime }}$, and a model selection procedure is provided with theoretical guarantees.