2020/12/31 by Siegfried Hörmann, Fatima Jammoul
Engineering · Mathematics · #Algorithm #Artificial intelligence #Autocorrelation #Computer science #Control Systems and Identification #Geodetic datum #Grid #Mathematics #Noise (video) #SIGNAL (programming language) #Smoothness #Statistical Methods and Inference #Statistical and numerical algorithms #Statistics #math.ST #stat.TH
paper · pdf · doi:10.1016/j.jmva.2021.104886
openalex publication_date 2021/11/09 · arxiv created 2021/11/15 · arxiv updated 2021/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In practice most functional data cannot be recorded on a continuum, but rather at discrete time points. It is also quite common that these measurements come with an additive error, which one would like eliminate for the statistical analysis. When the measurements for each functional datum are taken on the same grid, the underlying signal-plus-noise model can be viewed as a factor model. The signals refer to the common components of the factor model, the noise is related to the idiosyncratic components. We formulate a framework which allows to consistently recover the signal by a PCA based factor model estimation scheme. Our theoretical results hold under rather mild conditions, in particular we do not require specific smoothness assumptions for the underlying curves and allow for a certain degree of autocorrelation in the noise.