论文标题
$ f $ sensitivity模型下的灵敏度分析：分布鲁棒性的观点
Sensitivity analysis under the $f$-sensitivity models: a distributional robustness perspective
论文作者
论文摘要
本文介绍了$ f $ sensitivity模型，这是一种新的灵敏度模型，其特征是因果推断中违反不满意的。它假定由于无法衡量的混杂而导致的选择偏差是“平均”的；与文献中广泛使用的点灵敏度模型相比，它不仅可以通过其大小，而且遇到如此幅度的机会来捕获未衡量的混淆的强度。 我们根据分布鲁棒性的观点提出了一个在我们的新模型下进行灵敏度分析的框架。我们首先表明，在F-敏感性模型下，反事实手段的界限是针对新的分配稳健优化（DRO）程序的最佳解决方案，其双重形式本质上是风险最小化问题。然后，我们通过将新颖的伪造技术应用于相应的经验风险最小化（ERM）问题的输出来构建这些边界的点估计器。如果可以始终如一地估计我们的估计器，则显示出对反事实手段的有效界限，当ERM步骤又一致时，确切的界限。我们进一步建立了这些估计量的渐近正态性和WALD型推断，这些估计量低于估计的麻烦成分比根的收敛速率较慢。最后，通过数值实验证明了我们方法的性能。
This paper introduces the $f$-sensitivity model, a new sensitivity model that characterizes the violation of unconfoundedness in causal inference. It assumes the selection bias due to unmeasured confounding is bounded "on average"; compared with the widely used point-wise sensitivity models in the literature, it is able to capture the strength of unmeasured confounding by not only its magnitude but also the chance of encountering such a magnitude. We propose a framework for sensitivity analysis under our new model based on a distributional robustness perspective. We first show that the bounds on counterfactual means under the f-sensitivity model are optimal solutions to a new class of distributionally robust optimization (DRO) programs, whose dual forms are essentially risk minimization problems. We then construct point estimators for these bounds by applying a novel debiasing technique to the output of the corresponding empirical risk minimization (ERM) problems. Our estimators are shown to converge to valid bounds on counterfactual means if any nuisance component can be estimated consistently, and to the exact bounds when the ERM step is additionally consistent. We further establish asymptotic normality and Wald-type inference for these estimators under slower-than-root-n convergence rates of the estimated nuisance components. Finally, the performance of our method is demonstrated with numerical experiments.
