Preprocessing noisy functional data using factor models

We consider functional data which are measured on a discrete set of observation points. Often such data are measured with noise, and then the target is to recover the underlying signal. Most commonly, practitioners use some smoothing approach, e.g.,\ kernel smoothing or spline fitting towards this goal. The drawback of such curve fitting techniques is that they act function by function, and don't take into account information from the entire sample. In this paper we argue that signal and noise can be naturally represented as the common and idiosyncratic component, respectively, of a factor model. Accordingly, we propose to an estimation scheme which is based on factor models. The purpose of this paper is to explain the reasoning behind our approach and to compare its performance on simulated and on real data to competing methods.