  Functional data analysis is a fast evolving branch of modern statistics and
the functional linear model has become popular in recent years. However, most
estimation methods for this model rely on generalized least squares procedures
and therefore are sensitive to atypical observations. To remedy this, we
propose a two-step estimation procedure that combines robust functional
principal components and robust linear regression. Moreover, we propose a
transformation that reduces the curvature of the estimators and can be
advantageous in many settings. For these estimators we prove Fisher-consistency
at elliptical distributions and consistency under mild regularity conditions.
The influence function of the estimators is investigated as well. Simulation
experiments show that the proposed estimators have reasonable efficiency,
protect against outlying observations, produce smooth estimates and perform
well in comparison to existing approaches.
