Tail-Calibrated Estimation of Extreme Quantile Treatment Effects

2026-03-24

AI Summary

Existing methods for estimating extreme quantile treatment effects are often hindered by data sparsity in the tails or rely on strong assumptions about tail structure, limiting their ability to accurately assess causal effects of treatments on rare, high-impact events. This work proposes the Tail-calibrated Inverse Estimating Equation (TIEE) framework, which uniquely integrates extreme value theory with causal inference. By combining information across multiple quantile levels and anchoring the tail behavior using an extreme value model within a unified estimating equation, TIEE enables robust inference of extreme quantile treatment effects. The method demonstrates stability under various tail behaviors and model misspecifications, and has been successfully applied to causal attribution of extreme precipitation events in the Austrian Alps, confirming its practical utility in environmental risk assessment and related real-world applications.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Extreme quantile treatment effects (eQTEs) measure the causal impact of a treatment on the tails of an outcome distribution and are central for studying rare, high-impact events. Standard QTE methods often fail in extreme regimes due to data sparsity, while existing eQTE methods rely on restrictive tail assumptions or on interior-quantile theory. We propose the Tail-Calibrated Inverse Estimating Equation (TIEE) framework, which combines information across quantile levels and anchors the tail using extreme value models within a unified estimating equation approach. We establish asymptotic properties of the resulting estimator and evaluate its performance through simulation under different tail behaviours and model misspecifications. An application to extreme precipitation in the Austrian Alps illustrates how TIEE enables observational causal attribution for very rare events under anthropogenic warming. More broadly, the proposed framework establishes a new foundation for causal inference on rare, high-impact outcomes, with relevance across environmental risk, economics, and public health.

Problem

• extreme quantile treatment effects
• causal inference
• tail estimation
• rare events
• data sparsity

Innovation

• extreme quantile treatment effects
• tail calibration
• inverse estimating equation
• extreme value theory
• causal inference