A Location-Invariant Estimator of Extremal Quantile Treatment Effects for Heavy-Tailed Distributions
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.
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BibTeX
@misc{yu2026locationinvariant,
title = {{A Location-Invariant Estimator of Extremal Quantile Treatment Effects for Heavy-Tailed Distributions}},
author = {Xin Yu and Shuwei Huang and Jicheng Liu and Jielin Tang and Bolin Wang and Yunxiao Zhang and Tian Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04018},
eprint = {2609.04018},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04018},
}
RIS
TY - UNPB
TI - A Location-Invariant Estimator of Extremal Quantile Treatment Effects for Heavy-Tailed Distributions
AU - Xin Yu
AU - Shuwei Huang
AU - Jicheng Liu
AU - Jielin Tang
AU - Bolin Wang
AU - Yunxiao Zhang
AU - Tian Zhao
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04018
UR - https://arxiv.org/abs/2609.04018
AB - 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.
ER -