Optimal Algorithms for Nonlinear Estimation with Convex Models
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912786660982784 |
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| author | Foucart, Simon |
| author_facet | Foucart, Simon |
| contents | A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other simple functionals of the object can be optimally estimated by functionals of the observations that share a similar simple structure. This is established for the maximum of several linear functionals and even for the $\ell$th largest among them. Proving the latter requires an unusual refinement of the analytical Hahn--Banach theorem. The existence results are accompanied by practical recipes relying on convex optimization to construct the desired functionals, thereby justifying the term of estimation algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20826 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Algorithms for Nonlinear Estimation with Convex Models Foucart, Simon Functional Analysis Optimization and Control Statistics Theory A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other simple functionals of the object can be optimally estimated by functionals of the observations that share a similar simple structure. This is established for the maximum of several linear functionals and even for the $\ell$th largest among them. Proving the latter requires an unusual refinement of the analytical Hahn--Banach theorem. The existence results are accompanied by practical recipes relying on convex optimization to construct the desired functionals, thereby justifying the term of estimation algorithms. |
| title | Optimal Algorithms for Nonlinear Estimation with Convex Models |
| topic | Functional Analysis Optimization and Control Statistics Theory |
| url | https://arxiv.org/abs/2512.20826 |