Recent works have proposed regression models which are invariant across data collection environments. These estimators often have a causal interpretation under conditions on the environments and type of invariance imposed. One recent example, the Causal Dantzig (CD), is consistent under hidden confounding and represents an alternative to classical instrumental variable estimators such as Two Stage Least Squares (TSLS). In this work we derive the CD as a generalized method of moments (GMM) estimator. The GMM representation leads to several practical results, including 1) creation of the Generalized Causal Dantzig (GCD) estimator which can be applied to problems with continuous environments where the CD cannot be fit 2) a Hybrid (GCD-TSLS combination) estimator which has properties superior to GCD or TSLS alone 3) straightforward asymptotic results for all methods using GMM theory. We compare the CD, GCD, TSLS, and Hybrid estimators in simulations and an application to a Flow Cytometry data set. The newly proposed GCD and Hybrid estimators have superior performance to existing methods in many settings.

翻译：近期研究提出了跨数据采集环境保持不变的回归模型。此类估计量在特定环境条件与不变性约束下具有因果解释。最新范例——因果Dantzig（CD）方法可在存在隐藏混杂时保持一致性，并成为两阶段最小二乘法（TSLS）等经典工具变量估计量的替代方案。本文推导出CD方法作为广义矩估计（GMM）估计量的数学形式。GMM表示法带来多项实用成果：1）提出可应用于连续环境（CD方法无法适用）的广义因果Dantzig（GCD）估计量；2）构建兼具GCD与TSLS优势的混合估计量（GCD-TSLS组合），其性能优于单一方法；3）基于GMM理论为所有方法提供简洁的渐近结果。我们通过仿真实验及流式细胞术数据集应用，对CD、GCD、TSLS与混合估计量进行了比较。新提出的GCD及混合估计量在多数场景中展现出优于现有方法的性能。