标题： 对于$\ell_p$-损失，模型选择是否可能？ 回归模型的PCO估计 显示英文标题

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

摘要： 本文研究了当 $\xi$ 为次高斯分布时，序贯模型 $Y=\theta+\varepsilon\xi$ 中的模型选择问题，针对非欧几里得损失函数的情况。在该模型中，针对加权 $\ell_p$- 损失函数（$p\geq 1.$），研究了过拟合惩罚比较程序。通过次韦布尔变量的集中不等式，推导出若干个oracle不等式。利用精心设计的模型集合和惩罚项，得到了Besov体 $\mathcal{B}_{r,\infty}^s$ 的 minimax 收敛速度。这些结果被应用于非参数回归的功能模型。 显示英文摘要

摘要： 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.