论文标题
强大的非参数回归：审查和实际考虑
Robust nonparametric regression: review and practical considerations
论文作者
论文摘要
非参数回归模型提供了一种理解和量化变量之间关系的方法，而无需确定适当的可能回归功能的家族。尽管文献中已经提出了许多针对这些模型的估计方法，但大多数方法可能对训练集中的一小部分非典型观测值高度敏感。在本文中，我们回顾了非参数回归模型的异常鲁棒估计方法，特别注意实际考虑。由于离群值还可以通过影响带宽或平滑参数的选择来负面影响回归估计器，因此我们还讨论了此任务的可用鲁棒替代方案。最后，由于使用许多``经典''非参数回归估计器（及其强大的对应物）在具有适度或大量的解释变量的情况下可能非常具有挑战性，因此我们回顾了最新的强大非参数回归方法，这些方法随着越来越多的协方差量扩展，可以很好地扩展其范围。
Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have been proposed in the literature, most of them can be highly sensitive to the presence of a small proportion of atypical observations in the training set. In this paper we review outlier robust estimation methods for nonparametric regression models, paying particular attention to practical considerations. Since outliers can also influence negatively the regression estimator by affecting the selection of bandwidths or smoothing parameters, we also discuss available robust alternatives for this task. Finally, since using many of the ``classical'' nonparametric regression estimators (and their robust counterparts) can be very challenging in settings with a moderate or large number of explanatory variables, we review recent robust nonparametric regression methods that scale well with a growing number of covariates.
