Identification theory for causal effects in causal models associated with hidden variable directed acyclic graphs (DAGs) is well studied. However, the corresponding algorithms are underused due to the complexity of estimating the identifying functionals they output. In this work, we bridge the gap between identification and estimation of population-level causal effects involving a single treatment and a single outcome. We derive influence function based estimators that exhibit double robustness for the identified effects in a large class of hidden variable DAGs where the treatment satisfies a simple graphical criterion; this class includes models yielding the adjustment and front-door functionals as special cases. We also provide necessary and sufficient conditions under which the statistical model of a hidden variable DAG is nonparametrically saturated and implies no equality constraints on the observed data distribution. Further, we derive an important class of hidden variable DAGs that imply observed data distributions observationally equivalent (up to equality constraints) to fully observed DAGs. In these classes of DAGs, we derive estimators that achieve the semiparametric efficiency bounds for the target of interest where the treatment satisfies our graphical criterion. Finally, we provide a sound and complete identification algorithm that directly yields a weight based estimation strategy for any identifiable effect in hidden variable causal models.
翻译:对与隐藏的可变定向环绕图(DAGs)相关的因果关系模型的识别因果关系理论进行了充分研究,但是,由于估算其输出的功能的复杂性,相应的算法没有得到充分利用。在这项工作中,我们缩小了单一处理和单一结果所涉人口层面因果关系的识别和估计之间的差距。我们从基于影响的估算器中得出基于影响的功能,在大量隐藏的可变数据包中,该处理方法符合简单的图形标准;这一类包括产生调整和前门功能的模型,作为特殊案例。我们还提供了必要和充分的条件,使隐藏变量DAG的统计模型不具有对称饱和性,在所观察到的数据分布方面没有平等限制。此外,我们得出了一个重要的隐藏变量DAG,这意味着观测到的数据分布的观测值相当于(除平等制约外)完全观测到DAGs。在这些类别的DAGs中,我们从中得出了达到处理达到利息目标的半定量效率界限的模型,从而满足了我们的图表标准。我们提供了一种可识别的、完全的定量的模型。我们提供了一种可辨测测测算的模型,以任何可辨测测算的系数的模型。