Functional linear regression with Huber loss

In this paper, we consider the robust regression problem associated with Huber loss in the framework of functional linear model and reproducing kernel Hilbert spaces. We propose an Ivanov regularized empirical risk minimization estimation procedure to approximate the slope function of the linear model in the presence of outliers or heavy-tailed noises. By appropriately tuning the scale parameter of the Huber loss, we establish explicit rates of convergence for our estimates in terms of excess prediction risk under mild assumptions. Our study in the paper justifies the efficiency of Huber regression for functional data from a theoretical viewpoint.