# Estimation and Inference for Moments of Ratios with Robustness against Large Trimming Bias

arXiv: https://arxiv.org/abs/1709.00981 · HTML: https://mlsanity.com/paper/1709.00981/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2017.

## Built on by (most cited first, 3 of 3)

- [High Precision Causal Model Evaluation with Conditional Randomization](https://mlsanity.com/paper/2311.01902/) (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)

Empirical researchers often trim observations with small denominator A when they estimate moments of the form E[B/A]. Large trimming is a common practice to mitigate variance, but it incurs large trimming bias. This paper provides a novel method of correcting large trimming bias. If a researcher is willing to assume that the joint distribution between A and B is smooth, then a large trimming bias may be estimated well. With the bias correction, we also develop a valid and robust inference result for E[B/A].