Abstract:
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In this work, we bridge the gap between identification of causal effects in graphical models with unmeasured confounders and semiparametric estimation of the identified functionals. We derive influence function based estimators that exhibit double robustness for the identified effects in a large class of graphical models where the treatment satisfies a simple 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 underlying statistical model is nonparametrically saturated and implies no equality constraints on the observed data distribution. Further, we derive an important class of graphs that imply observed data distributions observationally equivalent (up to equality constraints) to fully observed directed acyclic graphs (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.
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