Minimax optimal subgroup identification
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AI 根据所提供的论文材料归类：摘要明确以 CATE、处理效应异质性、受益子群和最优处理规则为研究对象。
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极小极大最优的子群识别
- 研究问题
- 摘要研究如何识别条件平均处理效应超过给定阈值的人群，以及处理效应估计误差如何影响子群识别和治疗分配。
- 方法与思路
- 作者在无未观测混杂框架下对 CATE 估计值作阈值化，并结合不同 Hölder 光滑阶数及阈值附近的边际条件分析误差。
- 材料陈述的贡献
- 摘要称推导了水平集估计的渐近性质，并在所述光滑模型中识别极小极大最优估计量，辅以模拟和结肠手术应用。
- 阅读关注点
- 应核对水平集误差的损失定义、光滑性与边际条件如何共同决定速率，以及正阈值和资源约束之间的具体对应。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或期刊接收；摘要未列出完整识别条件、最优速率及手术应用结果。
原文摘要
Quantifying treatment effect heterogeneity is a crucial task in many areas of causal inference, e.g. optimal treatment allocation and estimation of subgroup effects. We study the problem of estimating the level sets of the conditional average treatment effect (CATE), identified under the no-unmeasured-confounders assumption. Given a user-specified threshold, the goal is to estimate the set of all units for whom the treatment effect exceeds that threshold. For example, if the cutoff is zero, the estimand is the set of all units who would benefit from receiving treatment. Assigning treatment just to this set represents the optimal treatment rule that maximises the mean population outcome. Similarly, cutoffs greater than zero represent optimal rules under resource constraints. The level set estimator that we study follows the plug-in principle and consists of simply thresholding a good estimator of the CATE. While many CATE estimators have been recently proposed and analysed, how their properties relate to those of the corresponding level set estimators remains unclear. Our first goal is thus to fill this gap by deriving the asymptotic properties of level set estimators depending on which estimator of the CATE is used. Next, we identify a minimax optimal estimator in a model where the CATE, the propensity score and the outcome model are Holder-smooth of varying orders. We consider data generating processes that satisfy a margin condition governing the probability of observing units for whom the CATE is close to the threshold. We investigate the performance of the estimators in simulations and illustrate our methods on a dataset used to study the effects on mortality of laparoscopic vs open surgery in the treatment of various conditions of the colon.