# The Empirical Likelihood Approach to Quantifying Uncertainty in Sample Average Approximation

arXiv: https://arxiv.org/abs/1604.02573 · HTML: https://mlsanity.com/paper/1604.02573/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2016.

## Built on by (most cited first, 12 of 12)

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- [A data-driven approach to beating SAA out-of-sample](https://mlsanity.com/paper/2105.12342/) (2021)
- [Understanding Deep Generative Models with Generalized Empirical Likelihoods](https://mlsanity.com/paper/2306.09780/) (2023)
- [Distributionally Robust Regularization of Sparse Integer Programming Trained Learning Models](https://mlsanity.com/paper/2311.01994/) (2023)
- [Ranking and Selection with Simultaneous Input Data Collection](https://mlsanity.com/paper/2503.11773/) (2025)
- [Statistical Guarantees for Distributionally Robust Optimization with Optimal Transport and OT-Regularized Divergences](https://mlsanity.com/paper/2603.27871/) (2026)

## Abstract (arXiv)

We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization problems with expected value objectives and constraints where the underlying probability distributions are observed via limited data. This approach relies on two distributionally robust optimization problems posited over the uncertain distribution, with a divergence-based uncertainty set that is suitably calibrated to provide asymptotic statistical guarantees.