标题： 选择异方差回归中的模型选择惩罚项 显示英文标题

标题： Choosing a penalty for model selection in heteroscedastic regression

摘要： 我们研究了在异方差数据的最小二乘回归中选择多个模型的问题。 我们证明，当惩罚函数是模型维度的函数时，任何惩罚程序都是次优的，至少对于一些典型的异方差模型选择问题而言。 特别是，Mallows 的 Cp 在此框架下是次优的。 相反，使用数据驱动的惩罚（如重采样或$V$折惩罚）可以实现最优模型选择。 因此，即使付出更高的计算成本，从数据中估计惩罚形状也是值得的。 模拟实验表明存在统计准确性与计算复杂性之间的权衡。 作为结论，我们概述了一些根据关于噪声水平可能变化的信息来选择惩罚的规则。 显示英文摘要

摘要： We consider the problem of choosing between several models in least-squares regression with heteroscedastic data. We prove that any penalization procedure is suboptimal when the penalty is a function of the dimension of the model, at least for some typical heteroscedastic model selection problems. In particular, Mallows' Cp is suboptimal in this framework. On the contrary, optimal model selection is possible with data-driven penalties such as resampling or $V$-fold penalties. Therefore, it is worth estimating the shape of the penalty from data, even at the price of a higher computational cost. Simulation experiments illustrate the existence of a trade-off between statistical accuracy and computational complexity. As a conclusion, we sketch some rules for choosing a penalty in least-squares regression, depending on what is known about possible variations of the noise-level.