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.

通过提出鲁棒性函数主成分和鲁棒线性回归结合的两步估计方法和一种可以减少估计曲率的转换，本研究在椭圆分布下证明了这些估计量的 Fisher 一致性和在温和正则性条件下的一致性，探究了这些估计量的影响函数，模拟实验表明，相比现有的方法，所提出的估计方法具有合理的效率、能够防止出现异常预测点、产生平滑的估计值，并表现良好。