针对重尾分布的极值分位数处理效应的位置不变估计量

中文摘要 AI 辅助

分位数处理效应（QTE）衡量处理对结果分布的影响，在目标分位数远超数据范围的应用中，其极值分位数水平的估计至关重要。对于重尾潜在结果，现有的极值QTE估计量依赖外推结合因果极值指数（EVI）估计量，但所得估计量在潜在结果分布发生常见位置偏移时不具备不变性，而总体QTE却具备该性质。我们分两步解决此问题：首先，利用逆倾向得分加权，将位置不变的Fraga EVI估计量适配到因果场景；其次，将原始外推公式替换为基于差值的方案，该方案在计算分位数差值时会抵消位置参数，因此所得QTE估计量具备位置不变性。我们证明了所提极值QTE估计量的相合性与渐近正态性，并提供了相合方差估计量，从而实现渐近有效的推断。模拟研究证实了所提方法的位置不变性、对阈值的稳定性以及覆盖性能。

英文摘要

Quantile treatment effects (QTEs) measure the effect of a treatment on the distribution of an outcome, and their estimation at extreme quantile levels is of central interest in applications where the target quantiles lie far beyond the range of the data. For heavy-tailed potential outcomes, existing extremal QTE estimators rely on extrapolation combined with a causal extreme value index (EVI) estimator, but the resulting estimator is not invariant under a common location shift of the potential outcome distributions, even though the population QTE is. We address this issue in two steps. First, we adapt the location-invariant Fraga estimator of the EVI to the causal setting using inverse propensity score weighting. Second, we replace the original extrapolation formula with a difference-based scheme, under which the location parameter cancels when quantile differences are taken. The resulting QTE estimator is therefore location invariant. We establish the consistency and asymptotic normality of the proposed extremal QTE estimators, and provide a consistent variance estimator, leading to asymptotically valid inference. A simulation study confirms the location invariance, the stability with respect to the threshold, and the coverage of the proposed methods.

发表机构

• Huazhong University of Science and Technology（华中科技大学）
• Tencent（腾讯）

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