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.
翻译:非参数回归模型提供了一种了解和量化变量之间关系的方式,而无需确定一个适当的可能的回归函数族。尽管文献中已经提出了许多这些模型的估计方法,但其中大多数方法对训练集中少量非典型观测的存在非常敏感。在本文中,我们综述了非参数回归模型的异常点鲁棒估计方法,并特别关注实际考虑。由于异常值也可能通过影响带宽或平滑参数的选择来对回归估计器产生负面影响,因此我们还讨论了可用的这种任务的鲁棒性替代方法。最后,由于在具有中等或大量解释变量的情况下使用许多“经典”非参数回归估计器(及其鲁棒对应物)可能非常具有挑战性,我们综述了最近可以很好地扩展到增加协变量的鲁棒非参数回归方法。