提出一种对位置变化不变的极端分位数处理效应估计方法,适用于重尾分布数据。
A location-invariant estimator of extremal quantile treatment effects for heavy-tailed distributions

- 采用逆倾向得分加权改进因果极值指数估计,实现位置不变性
- 用差值替代原外推公式,消除位置参数影响
- 在极端分位点上表现稳定,适合重尾分布的因果推断
分位数处理效应(QTE)衡量处理对结果分布的影响,极端分位点上的估计在目标分位数远超数据范围时尤为重要。对于重尾潜在结果,现有极端QTE估计器依赖外推与因果极值指数(EVI)估计,但其不满足位置不变性,尽管总体QTE具备该性质。本文通过两步解决:首先,将位置不变的Fraga EVI估计器推广至因果场景,使用逆倾向得分加权;其次,以差值法替代原始外推公式,使分位数差中的位置参数相消。由此得到的位置不变QTE估计量具有一致性和渐近正态性,并提供一致方差估计,支持渐近有效推断。模拟研究验证了方法的位置不变性、阈值稳定性及置信区间覆盖率。
原文摘要 · Abstract (English)
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.
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