Abstract
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 accord-ingly, by borrowing methods from factor model literature. We also show that principal components, which play a key role in functional data anal-ysis, can be accurately estimated by 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.
Original language | English |
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Pages (from-to) | 6232-6266 |
Number of pages | 35 |
Journal | Electronic Journal of Statistics |
Volume | 16 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2022 |
Keywords
- stat.ME
- stat.ML
- Functional data
- preprocessing
- signal-plus-noise
- factor models
- high-dimensional statistics
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty