The Empirical Likelihood Approach to Quantifying Uncertainty in Sample Average Approximation

2016/04/09 by Henry Lam, Enlu Zhou, Lam, Henry +1 · 1 citation
Decision Sciences · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Fuzzy Systems and Optimization #Methodology (stat.ME) #Probabilistic and Robust Engineering Design #Risk and Portfolio Optimization #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1604.02573

openalex publication_date 2016/04/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses
• Distributionally robust joint chance constraints with second-order moment information

Cited by

• Calibrating Decision Robustness via Inverse Conformal Risk Control

Related

• Optimization-based Quantification of Simulation Input Uncertainty via Empirical Likelihood
• Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach
• Recovering Best Statistical Guarantees via the Empirical Divergence-based Distributionally Robust Optimization
• Convergence and Bound Computation for Chance Constrained Distributionally Robust Models using Sample Approximation
• Nonparametric Estimation of Uncertainty Sets for Robust Optimization