Smoothing Splines Estimators in Functional Linear Regression with Errors-in-Variables

This work deals with a generalization of the Total Least Squaresmethod in the context of the functional linear model. We first propose asmoothing splines estimator of the functional coefficient of the model withoutnoise in the covariates and we obtain an asymptotic result for this estimator.Then, we adapt this estimator to the case where the covariates arenoisy and we also derive an upper bound for the convergence speed. Ourestimation procedure is evaluated by means of simulations.