The empirical likelihood approach to simulation input uncertainty

Abstract

We study the empirical likelihood method in constructing statistically accurate confidence bounds for stochastic simulation under nonparametric input uncertainty. The approach is based on positing a pair of distributionally robust optimization, with a suitably averaged divergence constraint over the uncertain input distributions, and calibrated with a χ2-quantile to provide asymptotic coverage guarantees. We present the theory giving rise to the constraint and the calibration. We also analyze the performance of our stochastic optimization algorithm. We numerically compare our approach with existing standard methods such as the bootstrap.