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关注这篇论文的作者
Guorong Dai

半监督与高维环境下处理效应估计的一般框架

研究问题
当少量样本观察到结局,而大量样本仅有处理和高维协变量时,如何利用未标记数据改善平均及分位数处理效应估计?
方法与思路
作者联合两类数据构造半监督估计量,分析双重稳健性、渐近正态性与效率,并研究加权核平滑辅助估计的收敛率。
材料陈述的贡献
摘要称倾向得分模型正确时可获得根号 n 一致性和渐近正态性;辅助函数均正确时达到半参数效率,并报告数值优势。
阅读关注点
应核对标记与未标记样本的分布关系、样本量及辅助估计误差条件,以及稳健性和效率比较所用的基准。
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这是预印本,同行评审或期刊接收未核实。摘要未完整列明抽样及速率条件,不能将所称优势推广到任意半监督数据。

原文摘要

In this article, we aim to provide a general and complete understanding of semi-supervised (SS) causal inference for treatment effects. Specifically, we consider two such estimands: (a) the average treatment effect and (b) the quantile treatment effect, as prototype cases, in an SS setting, characterized by two available data sets: (i) a labeled data set of size $n$, providing observations for a response and a set of high dimensional covariates, as well as a binary treatment indicator; and (ii) an unlabeled data set of size $N$, much larger than $n$, but without the response observed. Using these two data sets, we develop a family of SS estimators which are ensured to be: (1) more robust and (2) more efficient than their supervised counterparts based on the labeled data set only. Beyond the 'standard' double robustness results (in terms of consistency) that can be achieved by supervised methods as well, we further establish root-n consistency and asymptotic normality of our SS estimators whenever the propensity score in the model is correctly specified, without requiring specific forms of the nuisance functions involved. Such an improvement of robustness arises from the use of the massive unlabeled data, so it is generally not attainable in a purely supervised setting. In addition, our estimators are shown to be semi-parametrically efficient as long as all the nuisance functions are correctly specified. Moreover, as an illustration of the nuisance estimators, we consider inverse-probability-weighting type kernel smoothing estimators involving unknown covariate transformation mechanisms, and establish in high dimensional scenarios novel results on their uniform convergence rates, which should be of independent interest. Numerical results on both simulated and real data validate the advantage of our methods over their supervised counterparts with respect to both robustness and efficiency.

笔记与分组