Description
We consider noisy functional data $Y_t(s_i) = X_t(s_i) + \varepsilon_{ti}$ that has been recorded at a discrete set of observation points. Naturally, the goal is to recover the underlying signal $X_t$. Commonly, this is done by non-parametric smoothing approaches, e.g. kernel smoothing or spline fitting. These methods act function by function and do not take the overall presented information into consideration. We argue that it is often more accurate to take the entire data set into account, which can help recover systematic properties of the underlying signal. Other approaches using functional principal components do just that, but require strong assumptions on the smoothness of the underlying signal. We show that under very mild assumptions, the signal may be viewed as the common components of a factor model. Using this discovery, we develop a PCA driven approach to recover the signal and show consistency. 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. We demonstrate the applicability of our approach with simulation experiments and real life data analysis.| Period | 23 Jun 2021 → 25 Jun 2021 |
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| Event title | International Workshop on Functional and Operatorial Statistics |
| Event type | Conference |
| Conference number | 5 |
| Degree of Recognition | International |