Robust functional linear regression based on splines
Many existing methods for functional regression are based on the minimization of an L2 L 2 norm of the residuals and are therefore sensitive to atypical observations, which may affect the predictive power and/or the smoothness of the resulting estimate. A robust version of a spline-based estimate is presented, which has the form of an MM estimate, where the L2 L 2 loss is replaced by a bounded loss function. The estimate can be computed by a fast iterative algorithm. The proposed approach is compared, with favorable results, to the one based on L2 L 2 and to both classical and robust Partial Least Squares through an example with high-dimensional real data and a simulation study.1
mm estimate natural splines robust ridge estimator