# A Causal Bootstrap

arXiv: https://arxiv.org/abs/1807.02737 · HTML: https://mlsanity.com/paper/1807.02737/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2018.

## Built on by (most cited first, 4 of 4)

- [The Road to Explainability is Paved with Bias: Measuring the Fairness of Explanations](https://mlsanity.com/paper/2205.03295/) (2022)
- [Pulling Up by the Causal Bootstraps: Causal Data Augmentation for Pre-training Debiasing](https://mlsanity.com/paper/2108.12510/) (2021)
- [A Fast Bootstrap Algorithm for Causal Inference with Large Data](https://mlsanity.com/paper/2302.02859/) (2023)
- [Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap](https://mlsanity.com/paper/2301.05703/) (2023)

## Abstract (arXiv)

The bootstrap, introduced by Efron (1982), has become a very popular method for estimating variances and constructing confidence intervals. A key insight is that one can approximate the properties of estimators by using the empirical distribution function of the sample as an approximation for the true distribution function. This approach views the uncertainty in the estimator as coming exclusively from sampling uncertainty. We argue that for causal estimands the uncertainty arises entirely, or partially, from a different source, corresponding to the stochastic nature of the treatment received. We develop a bootstrap procedure that accounts for this uncertainty, and compare its properties to that of the classical bootstrap.