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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.05168 |
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| _version_ | 1866914614996893696 |
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| author | Ruiz-Medina, M. D. Torres-Signes, A. |
| author_facet | Ruiz-Medina, M. D. Torres-Signes, A. |
| contents | Under mild conditions, this paper derives a least-squares local linear Fréchet curve predictor for response and regressor evaluated in a separable Hilbert space. We obtain the conditions allowing the implementation of this local linear Fréchet functional predictor in the ambient L^{2}-space of vector functions, with values in the time-varying tangent space on a compact Riemannian manifold. An intrinsic local linear Fréchet curve predictor evaluated in such a manifold is secondly proposed, based on a weighted Fréchet mean approach. Its asymptotical optimality is proved. The simulation study and real-data application analyze the finite-sample performance of the empirical versions of both predictors, compared with a geodesic Nadaraya-Watson-type curve predictor. In the real-data application, the functional prediction of the time-varying spherical coordinates of the Earth's magnetic field is addressed, from the observation of the geocentric latitude and longitude of the satellite NASA's MAGSAT spacecraft. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamical local Fréchet curve regression in manifolds Ruiz-Medina, M. D. Torres-Signes, A. Statistics Theory Machine Learning Under mild conditions, this paper derives a least-squares local linear Fréchet curve predictor for response and regressor evaluated in a separable Hilbert space. We obtain the conditions allowing the implementation of this local linear Fréchet functional predictor in the ambient L^{2}-space of vector functions, with values in the time-varying tangent space on a compact Riemannian manifold. An intrinsic local linear Fréchet curve predictor evaluated in such a manifold is secondly proposed, based on a weighted Fréchet mean approach. Its asymptotical optimality is proved. The simulation study and real-data application analyze the finite-sample performance of the empirical versions of both predictors, compared with a geodesic Nadaraya-Watson-type curve predictor. In the real-data application, the functional prediction of the time-varying spherical coordinates of the Earth's magnetic field is addressed, from the observation of the geocentric latitude and longitude of the satellite NASA's MAGSAT spacecraft. |
| title | Dynamical local Fréchet curve regression in manifolds |
| topic | Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2505.05168 |