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We study the empirical likelihood approach to construct confidence intervalsfor the optimal value and the optimality gap of a given solution, henceforthquantify the statistical uncertainty of sample average approximation, foroptimization problems with expected value objectives and constraints where theunderlying probability distributions are observed via limited data. Thisapproach relies on two distributionally robust optimization problems positedover the uncertain distribution, with a divergence-based uncertainty set thatis suitably calibrated to provide asymptotic statistical guarantees.

The Empirical Likelihood Approach to Quantifying Uncertainty in Sample Average Approximation