Cross-validation in nonparametric regression with outliers
针对含异常值数据中标准交叉验证失效的问题，提出一种折扣极端预测误差的稳健交叉验证方法，用于核回归的带宽选择，并在大样本下证明其一致性，模拟实验显示效果良好。
A popular data-driven method for choosing the bandwidth in standard kernel regression is cross-validation. Even when there are outliers in the data, robust kernel regression can be used to estimate the unknown regression curve [Robust and Nonlinear Time Series Analysis. Lecture Notes in Statist. (1984) 26 163–184]. However, under these circumstances standard cross-validation is no longer a satisfactory bandwidth selector because it is unduly influenced by extreme prediction errors caused by the existence of these outliers. A more robust method proposed here is a cross-validation method that discounts the extreme prediction errors. In large samples the robust method chooses consistent bandwidths, and the consistency of the method is practically independent of the form in which extreme prediction errors are discounted. Additionally, evaluation of the method’s finite sample behavior in a simulation demonstrates that the proposed method performs favorably. This method can also be applied to other problems, for example, model selection, that require cross-validation.