Derivative Estimation of Multivariate Functional Data
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916497440374784 |
|---|---|
| author | Zhu, Yueyun Golovkine, Steven Bargary, Norma Simpkin, Andrew J. |
| author_facet | Zhu, Yueyun Golovkine, Steven Bargary, Norma Simpkin, Andrew J. |
| contents | Existing approaches for derivative estimation are restricted to univariate functional data. We propose two methods to estimate the principal components and scores for the derivatives of multivariate functional data. As a result, the derivatives can be reconstructed by a multivariate Karhunen-Loève expansion. The first approach is an extended version of multivariate functional principal component analysis (MFPCA) which incorporates the derivatives, referred to as derivative MFPCA (DMFPCA). The second approach is based on the derivation of multivariate Karhunen-Loève (DMKL) expansion. We compare the performance of the two proposed methods with a direct approach in simulations. The simulation results indicate that DMFPCA outperforms DMKL and the direct approach, particularly for densely observed data. We apply DMFPCA and DMKL methods to coronary angiogram data to recover derivatives of diameter and quantitative flow ratio. We obtain the multivariate functional principal components and scores of the derivatives, which can be used to classify patterns of coronary artery disease. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18398 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Derivative Estimation of Multivariate Functional Data Zhu, Yueyun Golovkine, Steven Bargary, Norma Simpkin, Andrew J. Methodology Existing approaches for derivative estimation are restricted to univariate functional data. We propose two methods to estimate the principal components and scores for the derivatives of multivariate functional data. As a result, the derivatives can be reconstructed by a multivariate Karhunen-Loève expansion. The first approach is an extended version of multivariate functional principal component analysis (MFPCA) which incorporates the derivatives, referred to as derivative MFPCA (DMFPCA). The second approach is based on the derivation of multivariate Karhunen-Loève (DMKL) expansion. We compare the performance of the two proposed methods with a direct approach in simulations. The simulation results indicate that DMFPCA outperforms DMKL and the direct approach, particularly for densely observed data. We apply DMFPCA and DMKL methods to coronary angiogram data to recover derivatives of diameter and quantitative flow ratio. We obtain the multivariate functional principal components and scores of the derivatives, which can be used to classify patterns of coronary artery disease. |
| title | Derivative Estimation of Multivariate Functional Data |
| topic | Methodology |
| url | https://arxiv.org/abs/2411.18398 |