A location-invariant estimator of extremal quantile treatment effects for heavy-tailed distributions

2026-09-03

AI Summary

针对重尾分布的极值分位数处理效应估计问题，通过改进Fraga估计器和使用基于差分的方法，提出了一种位置不变的估计方法。

Abstract

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.

Problem

• Quantile Treatment Effects
• Heavy-tailed Distributions
• Extremal Quantiles
• Location Invariance
• Causal Extreme Value Index

Innovation

• location-invariant
• extremal QTE
• heavy-tailed distributions
• inverse propensity score weighting
• difference-based scheme