Causal Inference for Heterogeneous Extreme Quantiles with Heavy-Tailed Outcomes
Abstract
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.
Related
- Factorial Multivariate Bayesian Causal Forests: heterogeneous main and interaction effects of multiple treatments on correlated outcomes
- Infinite Quantiles Inference under Local Differential Privacy
- Semiparametric inference for a Target Outcome Leveraging Heterogeneous External Summaries of Auxiliary Outcomes
- Flexible Doubly Robust Proximal Causal Inference for Censored Outcomes
- Sharp Design-based Inference for Quantiles of Individual Treatment Effects
BibTeX
@misc{wang2026causal,
title = {{Causal Inference for Heterogeneous Extreme Quantiles with Heavy-Tailed Outcomes}},
author = {Xiaorui Wang and Juan-Juan Cai and Huixia Judy Wang and Jian Qing Shi and Yanlin Tang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03933},
eprint = {2609.03933},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03933},
}
RIS
TY - UNPB
TI - Causal Inference for Heterogeneous Extreme Quantiles with Heavy-Tailed Outcomes
AU - Xiaorui Wang
AU - Juan-Juan Cai
AU - Huixia Judy Wang
AU - Jian Qing Shi
AU - Yanlin Tang
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03933
UR - https://arxiv.org/abs/2609.03933
AB - 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.
ER -