This paper considers estimation and inference for a class of varying coefficient models in which some of the responses and some of the covariates are missing at random and outliers are present. The paper proposes two general estimators—and a computationally attractive and asymptotically equivalent one-step version of them—that combine inverse probability weighting and robust local linear estimation. The paper also considers inference for the unknown infinite-dimensional parameter and proposes two Wald statistics that are shown to have power under a sequence of local Pitman drifts and are consistent as the drifts diverge. The results of the paper are illustrated with three examples: robust local generalized estimating equations, robust local quasi-likelihood and robust local nonlinear least squares estimation. A simulation study shows that the proposed estimators and test statistics have competitive finite sample properties, whereas two empirical examples illustrate the applicability of the proposed estimation and testing methods.

本文考虑了一类可变系数模型的估计和推断，在该模型中，某些响应和某些协变量在随机位置上缺失，并且存在离群值。本文提出了两个通用估计量，以及它们的计算吸引力和渐近等效的单步版本，它们结合了逆概率加权和鲁棒的局部线性估计。本文还考虑了未知的无穷维参数的推论，并提出了两个Wald统计量，这些统计量显示在一系列局部Pitman漂移下具有幂，并且在漂移发散时保持一致。本文的结果通过三个例子说明：鲁棒局部广义估计方程，鲁棒局部拟似然性和鲁棒局部非线性最小二乘估计。