# Inverting estimating equations for causal inference on quantiles

arXiv: https://arxiv.org/abs/2401.00987 · HTML: https://mlsanity.com/paper/2401.00987/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 32 references that are in the map.
- First posted on arXiv 2 Jan 2024.

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

- [Evaluating (weighted) dynamic treatment effects by double machine learning](https://mlsanity.com/paper/2012.00370/) (2020)
- [Multiply robust estimation of causal effects under principal ignorability](https://mlsanity.com/paper/2012.01615/) (2020)
- [Conditional Distribution Function Estimation Using Neural Networks for Censored and Uncensored Data](https://mlsanity.com/paper/2207.02384/) (2022)
- [Principal stratification analysis using principal scores](https://mlsanity.com/paper/1602.01196/) (2016)
- [Doubly robust estimation and sensitivity analysis for marginal structural quantile models](https://mlsanity.com/paper/2210.04100/) (2022)
- [Doubly Robust Estimation of Direct and Indirect Quantile Treatment Effects with Machine Learning](https://mlsanity.com/paper/2307.01049/) (2023)
- [Automatic Debiased Machine Learning for Dynamic Treatment Effects and General Nested Functionals](https://mlsanity.com/paper/2203.13887/) (2022)

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

- [Nonparametric efficient inference for network quantile causal effects under partial interference](https://mlsanity.com/paper/2604.13008/) (2026)

## Abstract (arXiv)

The causal inference literature frequently focuses on estimating the mean of the potential outcome, whereas quantiles of the potential outcome may carry important additional information. We propose a unified approach, based on the inverse estimating equations, to generalize a class of causal inference solutions from estimating the mean of the potential outcome to its quantiles. We assume that a moment function is available to identify the mean of the threshold-transformed potential outcome, based on which a convenient construction of the estimating equation of quantiles of potential outcome is proposed. In addition, we give a general construction of the efficient influence functions of the mean and quantiles of potential outcomes, and explicate their connection. We motivate estimators for the quantile estimands with the efficient influence function, and develop their asymptotic properties when either parametric models or data-adaptive machine learners are used to estimate the nuisance functions. A broad implication of our results is that one can rework the existing result for mean causal estimands to facilitate causal inference on quantiles. Our general results are illustrated by several analytical and numerical examples.