# Robust Inference Using Inverse Probability Weighting

arXiv: https://arxiv.org/abs/1810.11397 · HTML: https://mlsanity.com/paper/1810.11397/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2018.

## Built on by (most cited first, 14 of 14)

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- [Weight Clipping for Robust Conformal Inference under Unbounded Covariate Shifts](https://mlsanity.com/paper/2605.02072/) (2026)
- [Hypothesis testing for matched pairs with missing data by maximum mean discrepancy: An application to continuous glucose monitoring](https://mlsanity.com/paper/2206.01590/) (2022)
- [A Review and Roadmap of Deep Causal Model from Different Causal Structures and Representations](https://mlsanity.com/paper/2311.00923/) (2023)
- [Controlling for Unobserved Confounding with Large Language Model Classification of Patient Smoking Status](https://mlsanity.com/paper/2411.03004/) (2024)
- [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)
- [De-confounding Representation Learning for Counterfactual Inference on Continuous Treatment via Generative Adversarial Network](https://mlsanity.com/paper/2307.12625/) (2023)
- [VLUCI: Variational Learning of Unobserved Confounders for Counterfactual Inference](https://mlsanity.com/paper/2308.00904/) (2023)
- [Does Misclassifying Non-confounding Covariates as Confounders Affect the Causal Inference within the Potential Outcomes Framework?](https://mlsanity.com/paper/2308.11676/) (2023)
- [Integrating Active Learning in Causal Inference with Interference: A Novel Approach in Online Experiments](https://mlsanity.com/paper/2402.12710/) (2024)
- [Rate doubly robust estimation for weighted average treatment effects](https://mlsanity.com/paper/2509.14502/) (2025)
- [A Sensitivity Approach to Causal Inference Under Limited Overlap](https://mlsanity.com/paper/2511.22003/) (2025)
- [Disentangled Double Machine Learning for Accurate Causal Effect Estimation](https://mlsanity.com/paper/2605.24808/) (2026)

## Abstract (arXiv)

Inverse Probability Weighting (IPW) is widely used in empirical work in economics and other disciplines. As Gaussian approximations perform poorly in the presence of "small denominators," trimming is routinely employed as a regularization strategy. However, ad hoc trimming of the observations renders usual inference procedures invalid for the target estimand, even in large samples. In this paper, we first show that the IPW estimator can have different (Gaussian or non-Gaussian) asymptotic distributions, depending on how "close to zero" the probability weights are and on how large the trimming threshold is. As a remedy, we propose an inference procedure that is robust not only to small probability weights entering the IPW estimator but also to a wide range of trimming threshold choices, by adapting to these different asymptotic distributions. This robustness is achieved by employing resampling techniques and by correcting a non-negligible trimming bias. We also propose an easy-to-implement method for choosing the trimming threshold by minimizing an empirical analogue of the asymptotic mean squared error. In addition, we show that our inference procedure remains valid with the use of a data-driven trimming threshold. We illustrate our method by revisiting a dataset from the National Supported Work program.