# Minimax Rate-Optimal Inference for Individualized Quantile Treatment Effects in High-dimensional Models

arXiv: https://arxiv.org/abs/2503.18523 · HTML: https://mlsanity.com/paper/2503.18523/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2025.

## Built on by (most cited first, 1 of 1)

- [Direct Doubly Robust Estimation of Conditional Quantile Contrasts](https://mlsanity.com/paper/2601.19666/) (2026)

## Abstract (arXiv)

The quantification of treatment effects plays an important role in a wide range of applications, including policy making and bio-pharmaceutical research. In this article, we study the quantile treatment effect (QTE) while addressing two specific types of heterogeneities: (a) personalized heterogeneity, which captures the varying treatment effects for different individuals, and (b) quantile heterogeneity, which accounts for how the impact of covariates varies across different quantile levels. A well-designed debiased estimator for the individualized quantile treatment effect (IQTE) is proposed to capture such heterogeneities effectively. We show that this estimator converges weakly to a Gaussian process as a function of the quantile levels and propose valid statistical inference methods, including the construction of confidence intervals and the development of hypothesis testing decision rules. In addition, the minimax optimality frameworks for these inference procedures are established. Specifically, we derive the minimax optimal rates for the expected length of confidence intervals and the magnitude of the detection boundary for hypothesis testing procedures, illustrating the superiority of the proposed estimator. The effectiveness of our methods is demonstrated through extensive simulations and an analysis of the National Health and Nutrition Examination Survey (NHANES) datasets.