# Estimation and Inference of Extremal Quantile Treatment Effects for Heavy-Tailed Distributions

arXiv: https://arxiv.org/abs/2110.06627 · HTML: https://mlsanity.com/paper/2110.06627/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2021.

## Built on by (most cited first, 7 of 7)

- [Kernel PCA for multivariate extremes](https://mlsanity.com/paper/2211.13172/) (2022)
- [Cross-World Assumption and Refining Prediction Intervals for Individual Treatment Effects](https://mlsanity.com/paper/2507.12581/) (2025)
- [TSLiNGAM: DirectLiNGAM under heavy tails](https://mlsanity.com/paper/2308.05422/) (2023)
- [A Semiparametric Approach to Causal Inference](https://mlsanity.com/paper/2411.00950/) (2024)
- [Estimation of Treatment Effects in Extreme and Unobserved Data](https://mlsanity.com/paper/2506.14051/) (2025)
- [Stop Suppressing the Tail: Causal Inference for Extreme Events](https://mlsanity.com/paper/2605.27474/) (2026)
- [A Location-Invariant Estimator of Extremal Quantile Treatment Effects for Heavy-Tailed Distributions](https://mlsanity.com/paper/2609.04018/) (2026)

## Abstract (arXiv)

Causal inference for extreme events has many potential applications in fields such as climate science, medicine and economics. We study the extremal quantile treatment effect of a binary treatment on a continuous, heavy-tailed outcome. Existing methods are limited to the case where the quantile of interest is within the range of the observations. For applications in risk assessment, however, the most relevant cases relate to extremal quantiles that go beyond the data range. We introduce an estimator of the extremal quantile treatment effect that relies on asymptotic tail approximation, and use a new causal Hill estimator for the extreme value indices of potential outcome distributions. We establish asymptotic normality of the estimators and propose a consistent variance estimator to achieve valid statistical inference. We illustrate the performance of our method in simulation studies, and apply it to a real data set to estimate the extremal quantile treatment effect of college education on wage.