# Doubly Robust Estimation of Direct and Indirect Quantile Treatment Effects with Machine Learning

arXiv: https://arxiv.org/abs/2307.01049 · HTML: https://mlsanity.com/paper/2307.01049/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 3 Jul 2023.

## Builds on (most cited first, 7 of 7)

- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [The Influence Function of Semiparametric Estimators](https://mlsanity.com/paper/1508.01378/) (2015)
- [Program Evaluation and Causal Inference with High-Dimensional Data](https://mlsanity.com/paper/1311.2645/) (2013)
- [Visually Communicating and Teaching Intuition for Influence Functions](https://mlsanity.com/paper/1810.03260/) (2018)
- [Evaluating (weighted) dynamic treatment effects by double machine learning](https://mlsanity.com/paper/2012.00370/) (2020)
- [Tutorial: Deriving The Efficient Influence Curve for Large Models](https://mlsanity.com/paper/1903.01706/) (2019)
- [Semiparametric Estimation for Causal Mediation Analysis with Multiple Causally Ordered Mediators](https://mlsanity.com/paper/2011.12751/) (2020)

## Built on by (most cited first, 3 of 3)

- [Inverting estimating equations for causal inference on quantiles](https://mlsanity.com/paper/2401.00987/) (2024)
- [Testing Full Mediation of Treatment Effects and the Identifiability of Causal Mechanisms](https://mlsanity.com/paper/2603.04109/) (2026)
- [Nonparametric efficient inference for network quantile causal effects under partial interference](https://mlsanity.com/paper/2604.13008/) (2026)

## Abstract (arXiv)

We suggest double/debiased machine learning estimators of direct and indirect quantile treatment effects under a selection-on-observables assumption. This permits disentangling the causal effect of a binary treatment at a specific outcome rank into an indirect component that operates through an intermediate variable called mediator and an (unmediated) direct impact. The proposed method is based on the efficient score functions of the cumulative distribution functions of potential outcomes, which are robust to certain misspecifications of the nuisance parameters, i.e., the outcome, treatment, and mediator models. We estimate these nuisance parameters by machine learning and use cross-fitting to reduce overfitting bias in the estimation of direct and indirect quantile treatment effects. We establish uniform consistency and asymptotic normality of our effect estimators. We also propose a multiplier bootstrap for statistical inference and show the validity of the multiplier bootstrap. Finally, we investigate the finite sample performance of our method in a simulation study and apply it to empirical data from the National Job Corp Study to assess the direct and indirect earnings effects of training.