Smoothing splines estimators in functional linear regression with errors-in-variables

The total least squares method is generalized in the context of the functional linear model. A smoothing splines estimator of the functional coefficient of the model is first proposed without noise in the covariates and an asymptotic result for this estimator is obtained. Then, this estimator is adapted to the case where the covariates are noisy and an upper bound for the convergence speed is also derived. The estimation procedure is evaluated by means of simulations.