Preprocessing noisy functional data: a multivariate perspective
This work provides a more robust method for preprocessing noisy functional data, which is crucial for researchers and practitioners relying on accurate functional data analysis, by challenging the common iid noise assumption.
This paper addresses the challenge of noise in functional data, which are measured at discrete points. It demonstrates that by adopting a multivariate factor model perspective, the latent signal can be effectively estimated, leading to accurate estimation of principal components.
We consider functional data which are measured on a discrete set of observation points. Often such data are measured with additional noise. We explore in this paper the factor structure underlying this type of data. We show that the latent signal can be attributed to the common components of a corresponding factor model and can be estimated accordingly, by borrowing methods from factor model literature. We also show that principal components, which play a key role in functional data analysis, can be accurately estimated after taking such a multivariate instead of a `functional' perspective. In addition to the estimation problem, we also address testing of the null-hypothesis of iid noise. While this assumption is largely prevailing in the literature, we believe that it is often unrealistic and not supported by a residual analysis.