# Robust Generalized Method of Moments: A Finite Sample Viewpoint

arXiv: https://arxiv.org/abs/2110.03070 · HTML: https://mlsanity.com/paper/2110.03070/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 40 references that are in the map.
- First posted on arXiv 6 Oct 2021.

## Builds on (most cited first, 11 of 11)

- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Robust Estimators in High Dimensions without the Computational Intractability](https://mlsanity.com/paper/1604.06443/) (2016)
- [Sever: A Robust Meta-Algorithm for Stochastic Optimization](https://mlsanity.com/paper/1803.02815/) (2018)
- [Being Robust (in High Dimensions) Can Be Practical](https://mlsanity.com/paper/1703.00893/) (2017)
- [Robust Estimation via Robust Gradient Estimation](https://mlsanity.com/paper/1802.06485/) (2018)
- [Efficient Algorithms and Lower Bounds for Robust Linear Regression](https://mlsanity.com/paper/1806.00040/) (2018)
- [Sub-Gaussian estimators of the mean of a random vector](https://mlsanity.com/paper/1702.00482/) (2017)
- [Robust Linear Regression: Optimal Rates in Polynomial Time](https://mlsanity.com/paper/2007.01394/) (2020)
- [Empirical risk minimization for heavy-tailed losses](https://mlsanity.com/paper/1406.2462/) (2014)
- [Robust Regression via Mutivariate Regression Depth](https://mlsanity.com/paper/1702.04656/) (2017)
- [Robust Regression Revisited: Acceleration and Improved Estimation Rates](https://mlsanity.com/paper/2106.11938/) (2021)

## Built on by (most cited first, 1 of 1)

- [Robust Moment-Based Estimation via Spectral Gradient Reweighting](https://mlsanity.com/paper/2605.27718/) (2026)

## Abstract (arXiv)

For many inference problems in statistics and econometrics, the unknown parameter is identified by a set of moment conditions. A generic method of solving moment conditions is the Generalized Method of Moments (GMM). However, classical GMM estimation is potentially very sensitive to outliers. Robustified GMM estimators have been developed in the past, but suffer from several drawbacks: computational intractability, poor dimension-dependence, and no quantitative recovery guarantees in the presence of a constant fraction of outliers. In this work, we develop the first computationally efficient GMM estimator (under intuitive assumptions) that can tolerate a constant ε fraction of adversarially corrupted samples, and that has an ℓ2 recovery guarantee of O(√ε). To achieve this, we draw upon and extend a recent line of work on algorithmic robust statistics for related but simpler problems such as mean estimation, linear regression and stochastic optimization. As two examples of the generality of our algorithm, we show how our estimation algorithm and assumptions apply to instrumental variables linear and logistic regression. Moreover, we experimentally validate that our estimator outperforms classical IV regression and two-stage Huber regression on synthetic and semi-synthetic datasets with corruption.