The M-estimator for functional linear regression model

This paper considers the M-estimator for slope function in functional linear regression models. We approximate the slope function by minimizing the loss function based explicitly on functional principal components analysis, and the loss function can be chosen according to what we are estimating. Under mild assumptions, the convergence rate of the estimator of infinite dimensional slope function is derived. A simulation study is conducted to illustrate the numerical performance of the proposed M-estimator.