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Abstract：
Recent works have proposed regression models which are invariant across data collection environments [24, 20, 11, 16, 8]. 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.
摘要：
最近的工作已经提出了回归模型，这些模型在数据收集环境中是不变的[24，20，11，16，8]。这些估计器通常在环境和强加的不变性类型的条件下具有因果解释。最近的一个例子，原因Dantzig（CD），在隐藏的混杂条件下是一致的，并且代表了经典工具变量估计器的替代方法，例如两阶段最小二乘（TSLS）。在这项工作中，我们将CD导出为广义矩量法（GMM）估计器。GMM表示导致了几个实际结果，包括1）创建广义因果Dantzig（GCD）估计器，该估计器可应用于CD无法拟合的连续环境的问题2）混合（GCD-TSLS组合）估计器，其特性优于GCD或TSLS单独3）使用GMM理论的所有方法的简单渐近结果。我们比较CD，GCD,TSLS,和混合估计器在模拟中的应用，以及在流式细胞术数据集的应用。新提出的GCD和混合估计器在许多情况下具有优于现有方法的性能。
