论文标题
选择有条件仪器集的图形工具
Graphical tools for selecting conditional instrumental sets
论文作者
论文摘要
我们考虑使用条件仪器集的混淆，对总因果的总因果效应有效估计。具体而言，我们在线性结构方程模型的设置中考虑了具有相关误差的两阶段最小二乘估计器，该模型与已知的无环针混合图兼容。为了为我们的结果设定阶段，我们表征了线性有效的条件仪器集类别，这些仪器集得到了目标总效应的一致性两阶段最小二乘估计器，并为这些估计器得出了新的渐近方差公式。配备了这些结果，我们提供了三个图形工具，用于选择更有效的线性有效条件仪器集。首先，对于某些对线性有效的条件仪器集的图形标准，可以确定两个相应的估计量中的哪个具有较小的渐近方差。其次，一种贪婪地添加协变量的算法将渐近方差降低到给定有效的条件仪器集中。第三，一个线性有效的条件仪器集，相应的估计器具有最小的渐近方差，可以通过图形标准来确保。
We consider the efficient estimation of total causal effects in the presence of unmeasured confounding using conditional instrumental sets. Specifically, we consider the two-stage least squares estimator in the setting of a linear structural equation model with correlated errors that is compatible with a known acyclic directed mixed graph. To set the stage for our results, we characterize the class of linearly valid conditional instrumental sets that yield consistent two-stage least squares estimators for the target total effect and derive a new asymptotic variance formula for these estimators. Equipped with these results, we provide three graphical tools for selecting more efficient linearly valid conditional instrumental sets. First, a graphical criterion that for certain pairs of linearly valid conditional instrumental sets identifies which of the two corresponding estimators has the smaller asymptotic variance. Second, an algorithm that greedily adds covariates that reduce the asymptotic variance to a given linearly valid conditional instrumental set. Third, a linearly valid conditional instrumental set for which the corresponding estimator has the smallest asymptotic variance that can be ensured with a graphical criterion.
