Local polynomial estimation of regression operators from functional data with correlated errors

International audienceThis article considers the problem of nonparametric estimation of the regression operator $r$ in a functional regression model $Y=r(x)+\varepsilon$ with a scalar response $Y$, a functional explanatory variable $x$, and a second order stationary error process $\varepsilon$. We construct a local polynomial estimator of $r$ together with its Fréchet derivatives from functional data with correlated errors. The convergence in mean squared error of the constructed estimator is studied for both short and long range dependent error processes. Simulation studies on the performance of the proposed estimator are conducted, and applications to independent data and El Niño time series data are given