针对重尾结果的异质性极端分位数的因果推断

中文摘要 AI 辅助

针对具有重尾结果的观察性研究，我们提出了一个用于估计条件极端分位数处理效应（CEQTEs）的框架。我们的方法首先通过逆概率加权（IPW）分位数回归估计中间条件分位数，然后利用极值理论将其外推至极端水平。在线性条件分位数模型下，我们证明每个潜在结果的条件分布和边际分布共享一个共同的极值指数（EVI），由此分别基于条件信息和边际信息提出了两个互补的Hill型EVI估计量。在理论层面，我们引入了一种IPW尾部分位数得分过程，该过程结合了回归分位数得分过程和均匀尾部经验过程，并考虑了处理分配的影响。我们在温和的正则条件下建立了该过程的函数弱收敛性，且无需满足最大吸引域条件，这一结果为所提出的CEQTE估计量的渐近分析提供了概率基础。模拟研究表明该方法具有良好的有限样本性能，将其应用于NLSY79数据后发现，在由混杂因素定义的亚组中，大学教育对极高小时工资的影响存在显著异质性。

英文摘要

We propose a framework for estimating conditional extreme quantile treatment effects (CEQTEs) in observational studies with heavy-tailed outcomes. Our procedure first estimates intermediate conditional quantiles using inverse-probability-weighted (IPW) quantile regression and then extrapolates them to extreme levels using extreme value theory. Under a linear conditional quantile model, we show that the conditional and marginal distributions of each potential outcome share a common extreme value index (EVI), motivating two complementary Hill-type EVI estimators based on conditional and marginal information, respectively. On the theoretical front, we introduce an IPW tail quantile score process that bridges regression quantile score processes and uniform tail empirical processes while accounting for treatment assignment. We establish its functional weak convergence under mild regularity conditions, without requiring a max-domain-of-attraction condition. This result provides the probabilistic foundation for the asymptotic analysis of the proposed CEQTE estimators. Simulation studies demonstrate favorable finite-sample performance, and an application to NLSY79 data reveals substantial heterogeneity in the effect of college education on extremely high hourly wages across confounder-defined subpopulations.

发表机构

• Nanjing University of Information Science and Technology（南京信息工程大学）
• Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）
• Rice University（莱斯大学）
• Beijing Normal-Hong Kong Baptist University（北京师范大学-香港浸会大学联合国际学院）
• School of Statistics, East China Normal University（华东师范大学统计学院）

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