Pré-Publication, Document De Travail Année : 2025

Is model selection possible for the $\ell_p$-loss? PCO estimation for regression models

Résumé

This paper addresses the problem of model selection in the sequence model $Y=\theta+\varepsilon\xi$, when $\xi$ 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.

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Dates et versions

hal-05035155 , version 1 (15-04-2025)

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  • HAL Id : hal-05035155 , version 1

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Claire Lacour, Pascal Massart, Vincent Rivoirard. Is model selection possible for the $\ell_p$-loss? PCO estimation for regression models. 2025. ⟨hal-05035155⟩
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