# Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness

arXiv: https://arxiv.org/abs/1712.04594 · HTML: https://mlsanity.com/paper/1712.04594/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2017.

## Built on by (most cited first, 11 of 11)

- [Finite Sample Analysis of Minimax Offline Reinforcement Learning: Completeness, Fast Rates and First-Order Efficiency](https://mlsanity.com/paper/2102.02981/) (2021)
- [Off-policy estimation of linear functionals: Non-asymptotic theory for semi-parametric efficiency](https://mlsanity.com/paper/2209.13075/) (2022)
- [β-Intact-VAE: Identifying and Estimating Causal Effects under Limited Overlap](https://mlsanity.com/paper/2110.05225/) (2021)
- [Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency](https://mlsanity.com/paper/2301.06240/) (2023)
- [Constructing Confidence Intervals for Average Treatment Effects from Multiple Datasets](https://mlsanity.com/paper/2412.11511/) (2024)
- [Double Robust Bayesian Inference on Average Treatment Effects](https://mlsanity.com/paper/2211.16298/) (2022)
- [Off-policy estimation with adaptively collected data: the power of online learning](https://mlsanity.com/paper/2411.12786/) (2024)
- [Tight Non-asymptotic Inference via Sub-Gaussian Intrinsic Moment Norm](https://mlsanity.com/paper/2303.07287/) (2023)
- [Causal Effect Regularization: Automated Detection and Removal of Spurious Attributes](https://mlsanity.com/paper/2306.11072/) (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)
- [A Sensitivity Approach to Causal Inference Under Limited Overlap](https://mlsanity.com/paper/2511.22003/) (2025)

## Abstract (arXiv)

We consider estimation and inference on average treatment effects under unconfoundedness conditional on the realizations of the treatment variable and covariates. Given nonparametric smoothness and/or shape restrictions on the conditional mean of the outcome variable, we derive estimators and confidence intervals (CIs) that are optimal in finite samples when the regression errors are normal with known variance. In contrast to conventional CIs, our CIs use a larger critical value that explicitly takes into account the potential bias of the estimator. When the error distribution is unknown, feasible versions of our CIs are valid asymptotically, even when √n-inference is not possible due to lack of overlap, or low smoothness of the conditional mean. We also derive the minimum smoothness conditions on the conditional mean that are necessary for √n-inference. When the conditional mean is restricted to be Lipschitz with a large enough bound on the Lipschitz constant, the optimal estimator reduces to a matching estimator with the number of matches set to one. We illustrate our methods in an application to the National Supported Work Demonstration.