FWF - FUNAFA - Analysing functional data by approximate factor models

Functional data are commonly observed on a discrete set of observation points. Often the measurements are noisy (e.g. due to measurement errors) and then the target is to recover the underlying latent “signal”. In preliminary research we have shown that the signal can be identified as the common component of an approximate factor model. The purpose of this project is then to use this structure and propose an alternative method to existing preprocessing tools. Most of these tools are based on smoothing techniques and act “function-by-function”, i.e. they do not take into account the information of the entire sample and require stringent regularity conditions for the underlying signal. In this project we explore how factor models can overcome these deficiencies.