Robust Estimation for Generalized Additive Models

This article studies <i>M</i>-type estimators for fitting robust generalized additive models in the presence of anomalous data. A new theoretical construct is developed to connect the costly <i>M</i>-type estimation with least-squares type calculations. Its asymptotic properties are studied and used to motivate a computational algorithm. The main idea is to decompose the overall <i>M</i>-type estimation problem into a sequence of well-studied conventional additive model fittings. The resulting algorithm is fast and stable, can be paired with different nonparametric smoothers, and can also be applied to cases with multiple covariates. As another contribution of this article, automatic methods for smoothing parameter selection are proposed. These methods are designed to be resistant to outliers. The empirical performance of the proposed methodology is illustrated via both simulation experiments and real data analysis. Supplementary materials are available online.

本文针对存在异常数据的场景，研究了用于拟合稳健广义可加模型（generalized additive models）的M型估计器（M-type estimators）。本文提出一种全新的理论构造，用以将计算成本高昂的M型估计与最小二乘类计算相联结。针对该理论构造的渐近性质展开研究，并以此为基础推导得到一款计算算法。其核心思路是将整体M型估计问题拆解为一系列经广泛研究的传统可加模型拟合任务。所得到的算法兼具高效性与稳定性，可与多种非参数平滑器（nonparametric smoothers）结合使用，同时也可推广至多协变量（covariates）场景。作为本文的另一项贡献，本文提出了用于平滑参数选择的自动化方法，这类方法具备抵御异常值干扰的特性。本文通过仿真实验与真实数据分析，验证了所提方法论的实证表现。本文附带的补充材料可在线获取。