Variance Reduction for Causal Inference
因果推断中的方差降低AI 解读 ↓
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因果推断中的方差降低
- 研究问题
- 估计平均处理效应时，加入工具变量或仅预测结果的协变量分别怎样影响效率，以及已知倾向得分下能否构造便于计算的调整估计量？
- 方法与思路
- 作者分析不同协变量角色对渐近方差的影响，并在使用已知倾向得分的逆概率加权估计量上加入线性修正，开展理论与数值研究。
- 材料陈述的贡献
- 摘要称，满足结果排除限制的额外工具变量会损害效率，结果预测变量可降低方差；提出的线性修正估计量在所述一般情形下接近有效。
- 阅读关注点
- 应核对方差比较的识别与正则条件、倾向得分何时可视为已知、线性修正的具体形式，以及接近有效所采用的衡量标准。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未给出完整条件或效率差距，已知倾向得分方法的适用场景也需核对。
原文摘要
Propensity score methods have been shown to be powerful in obtaining efficient estimators of average treatment effect (ATE) from observational data, especially under the existence of confounding factors. When estimating, deciding which type of covariates need to be included in the propensity score function is important, since incorporating some unnecessary covariates may amplify both bias and variance of estimators of ATE. In this paper, we show that including additional instrumental variables that satisfy the exclusion restriction for outcome will do harm to the statistical efficiency. Also, we prove that, controlling for covariates that appear as outcome predictors, i.e. predict the outcomes and are irrelevant to the exposures, can help reduce the asymptotic variance of ATE estimation. We also note that, efficiently estimating the ATE by non-parametric or semi-parametric methods require the estimated propensity score function, as described in Hirano et al. (2003)\cite{Hirano2003}. Such estimation procedure usually asks for many regularity conditions, Rothe (2016)\cite{Rothe2016} also illustrated this point and proposed a known propensity score (KPS) estimator that requires mild regularity conditions and is still fully efficient. In addition, we introduce a linearly modified (LM) estimator that is nearly efficient in most general settings and need not estimation of the propensity score function, hence convenient to calculate. The construction of this estimator borrows idea from the interaction estimator of Lin (2013)\cite{Lin2013}, in which regression adjustment with interaction terms are applied to deal with data arising from a completely randomized experiment. As its name suggests, the LM estimator can be viewed as a linear modification on the IPW estimator using known propensity scores. We will also investigate its statistical properties both analytically and numerically.