Structural adaptation and rate accelerated estimation in bivariate functional data
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918478443708416 |
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| author | Kassi, Omar Wang, Sunny G. W. |
| author_facet | Kassi, Omar Wang, Sunny G. W. |
| contents | We introduce directional regularity, a new definition of anisotropy for multivariate functional data. Instead of taking the conventional view, which determines anisotropy as a notion of smoothness along a dimension, directional regularity additionally views anisotropy through the lens of directions. We show that faster rates of convergence for smoothing can be obtained through a change-of-basis by adapting to the anisotropy of a bivariate process. An algorithm for the estimation and identification of the change-of-basis matrix is constructed, made possible due to the replication structure of functional data. Non-asymptotic bounds are provided for our algorithm, supplemented by numerical evidence from an extensive simulation study. Finally, a real-world rainfall measurement dataset is analyzed with our methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00817 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Structural adaptation and rate accelerated estimation in bivariate functional data Kassi, Omar Wang, Sunny G. W. Methodology Statistics Theory Machine Learning We introduce directional regularity, a new definition of anisotropy for multivariate functional data. Instead of taking the conventional view, which determines anisotropy as a notion of smoothness along a dimension, directional regularity additionally views anisotropy through the lens of directions. We show that faster rates of convergence for smoothing can be obtained through a change-of-basis by adapting to the anisotropy of a bivariate process. An algorithm for the estimation and identification of the change-of-basis matrix is constructed, made possible due to the replication structure of functional data. Non-asymptotic bounds are provided for our algorithm, supplemented by numerical evidence from an extensive simulation study. Finally, a real-world rainfall measurement dataset is analyzed with our methods. |
| title | Structural adaptation and rate accelerated estimation in bivariate functional data |
| topic | Methodology Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2409.00817 |