Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

We address new challenges related to non parametric estimation when the data are of complex nature (massive, sequentially observed and infinite dimensional).  We focus on online estimation of the regression and  variance operators, when the response $Y$ is a real random variable and the covariate $X$ takes values in an infinite-dimensional space. Estimators are  introduced when a sample  is supposed to be sequentially collected from a functional regression model. Asymptotic results are established with convergence rates, whereas some applications  show how the proposed estimators perform in terms of reducing the computational time without decreasing significantly the accuracy.