# Asymptotic causal inference with observational studies trimmed by the estimated propensity scores

arXiv: https://arxiv.org/abs/1704.00666 · HTML: https://mlsanity.com/paper/1704.00666/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2017.

## Built on by (most cited first, 2 of 2)

- [Double Robust Semi-Supervised Inference for the Mean: Selection Bias under MAR Labeling with Decaying Overlap](https://mlsanity.com/paper/2104.06667/) (2021)
- [Constructing optimal treatment length strategies to maximize quality-adjusted lifetimes](https://mlsanity.com/paper/2412.05108/) (2024)

## Abstract (arXiv)

Causal inference with observational studies often relies on the assumptions of unconfoundedness and overlap of covariate distributions in different treatment groups. The overlap assumption is violated when some units have propensity scores close to 0 or 1, and therefore both practical and theoretical researchers suggest dropping units with extreme estimated propensity scores. However, existing trimming methods ignore the uncertainty in this design stage and restrict inference only to the trimmed sample, due to the non-smoothness of the trimming. We propose a smooth weighting, which approximates the existing sample trimming but has better asymptotic properties. An advantage of the new smoothly weighted estimator is its asymptotic linearity, which ensures that the bootstrap can be used to make inference for the target population, incorporating uncertainty arising from both the design and analysis stages. We also extend the theory to the average treatment effect on the treated, suggesting trimming samples with estimated propensity scores close to 1.