Abstract: We investigate the theoretical properties of robust estimators for the regression coefficient function in functional linear regression. A robust procedure is provided in which we use outlier-resistant loss functions including non-convex loss functions. Their robust estimates are computed using an iteratively reweighted penalized least-squares algorithm. Using a pseudo data approach, we are able to show that our robust estimators also achieve the same convergence rate for prediction and estimation as the penalized least squares estimator does in the classical functional linear regression. Theoretical developments are demonstrated using numerical studies with various types of robust loss, illustrating the merit of the method.

Key words and phrases: M-type smoothing splines, outlier-resistant loss function, reproducing kernel Hilbert space, robust functional linear regression.