Is model selection possible for the $\ell_p$-loss? PCO estimation for regression models
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| Format: | Preprint |
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2025
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| _version_ | 1866908320597540864 |
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| author | Lacour, Claire Massart, Pascal Rivoirard, Vincent |
| author_facet | Lacour, Claire Massart, Pascal Rivoirard, Vincent |
| contents | This paper addresses the problem of model selection in the sequence model $Y=θ+\varepsilonξ$, when $ξ$ is sub-Gaussian, for non-euclidian loss-functions. In this model, the Penalized Comparison to Overfitting procedure is studied for the weighted $\ell_p$-loss, $p\geq 1.$ Several oracle inequalities are derived from concentration inequalities for sub-Weibull variables. Using judicious collections of models and penalty terms, minimax rates of convergence are stated for Besov bodies $\mathcal{B}_{r,\infty}^s$. These results are applied to the functional model of nonparametric regression. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_11217 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Is model selection possible for the $\ell_p$-loss? PCO estimation for regression models Lacour, Claire Massart, Pascal Rivoirard, Vincent Statistics Theory 62G05, 62C20 (Primary) 62G08, 60E15 (Secondary) This paper addresses the problem of model selection in the sequence model $Y=θ+\varepsilonξ$, when $ξ$ is sub-Gaussian, for non-euclidian loss-functions. In this model, the Penalized Comparison to Overfitting procedure is studied for the weighted $\ell_p$-loss, $p\geq 1.$ Several oracle inequalities are derived from concentration inequalities for sub-Weibull variables. Using judicious collections of models and penalty terms, minimax rates of convergence are stated for Besov bodies $\mathcal{B}_{r,\infty}^s$. These results are applied to the functional model of nonparametric regression. |
| title | Is model selection possible for the $\ell_p$-loss? PCO estimation for regression models |
| topic | Statistics Theory 62G05, 62C20 (Primary) 62G08, 60E15 (Secondary) |
| url | https://arxiv.org/abs/2504.11217 |