Nonparametric Estimation from Correlated Copies of a Drifted Process
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915736520228864 |
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| author | Marie, Nicolas |
| author_facet | Marie, Nicolas |
| contents | This paper presents several situations leading to the observation of multiple correlated copies of a drifted process, and then non-asymptotic risk bounds are established on nonparametric estimators of the drift function $b_0$ and its derivative. For drifted Gaussian processes with a regular enough covariance function, a sharper risk bound is established on the estimator of $b_0'$, and a model selection procedure is provided with theoretical guarantees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05259 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonparametric Estimation from Correlated Copies of a Drifted Process Marie, Nicolas Statistics Theory This paper presents several situations leading to the observation of multiple correlated copies of a drifted process, and then non-asymptotic risk bounds are established on nonparametric estimators of the drift function $b_0$ and its derivative. For drifted Gaussian processes with a regular enough covariance function, a sharper risk bound is established on the estimator of $b_0'$, and a model selection procedure is provided with theoretical guarantees. |
| title | Nonparametric Estimation from Correlated Copies of a Drifted Process |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2508.05259 |