Bias-Reduced Doubly Robust Estimation

Over the past decade, doubly robust estimators have been proposed for a variety of target parameters in causal inference and missing data models. These are asymptotically unbiased when at least one of two nuisance working models is correctly specified, regardless of which. While their asymptotic distribution is not affected by the choice of root-n consistent estimators of the nuisance parameters indexing these working models when all working models are correctly specified, this choice of estimators can have a dramatic impact under misspecification of at least one working model. In this article, we will therefore propose a simple and generic estimation principle for the nuisance parameters indexing each of the working models, which is designed to improve the performance of the doubly robust estimator of interest, relative to the default use of maximum likelihood estimators for the nuisance parameters. The proposed approach locally minimizes the squared first-order asymptotic bias of the doubly robust estimator under misspecification of both working models and results in doubly robust estimators with easy-to-calculate asymptotic variance. It moreover improves the stability of the weights in those doubly robust estimators which invoke inverse probability weighting. Simulation studies confirm the desirable finite-sample performance of the proposed estimators. Supplementary materials for this article are available online.

过去十余年间，双重稳健估计量（doubly robust estimators）已被提出用于因果推断与缺失数据模型中的各类目标参数。当两个扰动工作模型中至少有一个设定正确时，此类估计量具备渐近无偏性，且与具体哪一个模型设定正确无关。当所有工作模型均设定正确时，为这些工作模型所对应的扰动参数构建的√n相合估计量的选择，不会影响其渐近分布；但当至少一个工作模型设定错误时，该估计量的选择会对结果产生显著影响。因此，本文将针对各工作模型对应的扰动参数，提出一种简洁通用的估计原则，旨在相较于默认使用的极大似然估计量，提升目标双重稳健估计量的性能。所提方法可在两个工作模型均设定错误的场景下，局部最小化双重稳健估计量的一阶渐近偏差的平方，同时得到易于计算渐近方差的双重稳健估计量。此外，该方法还可提升那些采用逆概率加权（inverse probability weighting）的双重稳健估计量中权重的稳定性。模拟研究证实了所提估计量具备优异的有限样本性能。本文的补充材料可在线获取。