Estimation of a score-explained non-randomized treatment effect in fixed and high dimensions
固定维与高维下由评分解释的非随机处理效应估计AI 解读 ↓
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固定维与高维下由评分解释的非随机处理效应估计
- 研究问题
- 当处理分配依据某个评分，且评分可由个体特征解释时，能否在存在混杂的非随机处理系统中，以根号样本量速率估计处理效应？
- 方法与思路
- 作者提出 SCENTS 模型及估计方法，分析固定维下的渐近性质，再通过去偏程序构造高维估计量，并用两项实际数据进行比较。
- 材料陈述的贡献
- 摘要称，估计量具有根号样本量收敛率和渐近正态性，正态误差下半参数有效；高维版本也具有相应速率，并可扩展至含噪部分线性模型。
- 阅读关注点
- 核对评分解释结构如何实现识别、允许何种混杂，以及误差分布、高维去偏和含噪变量扩展各自需要哪些条件与收敛要求。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未获核实；摘要未列出具体识别及高维条件，根号样本量速率不能推广至任意非随机处理。
原文摘要
Non-randomized treatment effect models are widely used for the assessment of treatment effects in various fields and in particular social science disciplines like political science, psychometry, psychology. More specifically, these are situations where treatment is assigned to an individual based on some of their characteristics (e.g. scholarship is allocated based on merit or antihypertensive treatments are allocated based on blood pressure level) instead of being allocated randomly, as is the case, for example, in randomized clinical trials. Popular methods that have been largely employed till date for estimation of such treatment effects suffer from slow rates of convergence (i.e. slower than $\sqrt{n}$). In this paper, we present a new model coined SCENTS: Score Explained Non-Randomized Treatment Systems, and a corresponding method that allows estimation of the treatment effect at $\sqrt{n}$ rate in the presence of fairly general forms of confoundedness, when the `score' variable on whose basis treatment is assigned can be explained via certain feature measurements of the individuals under study. We show that our estimator is asymptotically normal in general and semi-parametrically efficient under normal errors. We further extend our analysis to high dimensional covariates and propose a $\sqrt n$ consistent and asymptotically normal estimator based on a de-biasing procedure. Our analysis for the high dimensional incarnation can be readily extended to analyze partial linear models in the presence of noisy variables corresponding to the non-linear part of the model, where the noise can be correlated with the variables corresponding to the linear part. We analyze two real datasets via our method and compare our results with those obtained by using previous approaches. We conclude this paper with a discussion on some possible extensions of our approach.