# Some Doubly and Multiply Robust Estimators of Controlled Direct Effects

arXiv: https://arxiv.org/abs/2011.09569 · HTML: https://mlsanity.com/paper/2011.09569/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2020.

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

- [Causal Decomposition Analysis with Synergistic Interventions: A Triply-Robust Machine Learning Approach to Addressing Multiple Dimensions of Social Disparities](https://mlsanity.com/paper/2506.18994/) (2025)

## Abstract (arXiv)

This letter introduces several doubly, triply, and quadruply robust estimators of the controlled direct effect. Among them, the triply and quadruply robust estimators are locally semiparametric efficient, and well suited to the use of data-adaptive methods for estimating their nuisance functions.