Explaining Practical Differences Between Treatment Effect Estimators with High Dimensional Asymptotics
用高维渐近理论解释处理效应估计器的实际差异AI 解读 ↓
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用高维渐近理论解释处理效应估计器的实际差异
- 研究问题
- 在混杂变量完全观测且维度与样本量同阶时，为何 G 计算、IPW、AIPW 与 TMLE 的实际偏差和方差可能明显不同？
- 方法与思路
- 作者以处理分配和结果的广义线性模型作为机器学习调整的代理设定，在高维渐近框架中保留第一阶段估计带来的非消失方差。
- 材料陈述的贡献
- 摘要称高维理论能解释经典一阶渐近分析掩盖的性能差异；当结果模型估计偏差较小时，G 计算和 TMLE 的偏差与方差表现更好。
- 阅读关注点
- 应核对广义线性模型、维度比例和第一阶段拟合设定，明确结果模型低偏差条件，并检查方差展开与各估计器比较成立的范围。
- 阅读边界
- 所给版本为 arXiv 预印本，未核实同行评审或接收；摘要未给完整参数假设和比较公式，结论不能直接推广至任意机器学习方法。
原文摘要
We revisit the classical causal inference problem of estimating the average treatment effect in the presence of fully observed confounding variables using two-stage semiparametric methods. In existing theoretical studies of methods such as G-computation, inverse propensity weighting (IPW), and two common doubly robust estimators -- augmented IPW (AIPW) and targeted maximum likelihood estimation (TMLE) -- they are either bias-dominated, or have similar asymptotic statistical properties. However, when applied to real datasets, they often appear to have notably different variance. We compare these methods when using a machine learning (ML) model to estimate the nuisance parameters of the semiparametric model, and highlight some of the important differences. When the outcome model estimates have little bias, which is common among some key ML models, G-computation and the TMLE outperforms the other estimators in both bias and variance. We show that the differences can be explained using high-dimensional statistical theory, where the number of confounders $d$ is of the same order as the sample size $n$. To make this theoretical problem tractable, we posit a generalized linear model for the effect of the confounders on the treatment assignment and outcomes. Despite making parametric assumptions, this setting is a useful surrogate for some machine learning methods used to adjust for confounding in two-stage semiparametric methods. In particular, the estimation of the first stage adds variance that does not vanish, forcing us to confront terms in the asymptotic expansion that normally are brushed aside as finite sample defects. However, our model emphasizes differences in performance between these estimators beyond first-order asymptotics.