Principal Component Analysis of Two-dimensional Functional Data with Serial Correlation
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916184655396864 |
|---|---|
| author | Shen, Shirun Zhou, Huiya He, Kejun Zhou, Lan |
| author_facet | Shen, Shirun Zhou, Huiya He, Kejun Zhou, Lan |
| contents | In this paper, we propose a novel model to analyze serially correlated two-dimensional functional data observed sparsely and irregularly on a domain which may not be a rectangle. Our approach employs a mixed effects model that specifies the principal component functions as bivariate splines on triangulations and the principal component scores as random effects which follow an auto-regressive model. We apply the thin-plate penalty for regularizing the bivariate function estimation and develop an effective EM algorithm along with Kalman filter and smoother for calculating the penalized likelihood estimates of the parameters. Our approach was applied on simulated datasets and on Texas monthly average temperature data from January year 1915 to December year 2014. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_04408 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Principal Component Analysis of Two-dimensional Functional Data with Serial Correlation Shen, Shirun Zhou, Huiya He, Kejun Zhou, Lan Methodology In this paper, we propose a novel model to analyze serially correlated two-dimensional functional data observed sparsely and irregularly on a domain which may not be a rectangle. Our approach employs a mixed effects model that specifies the principal component functions as bivariate splines on triangulations and the principal component scores as random effects which follow an auto-regressive model. We apply the thin-plate penalty for regularizing the bivariate function estimation and develop an effective EM algorithm along with Kalman filter and smoother for calculating the penalized likelihood estimates of the parameters. Our approach was applied on simulated datasets and on Texas monthly average temperature data from January year 1915 to December year 2014. |
| title | Principal Component Analysis of Two-dimensional Functional Data with Serial Correlation |
| topic | Methodology |
| url | https://arxiv.org/abs/2303.04408 |