Nonparametric Input-Output Uncertainty Comparisons

We consider the problem of inferring the system with the best simulation output mean among k systems when the simulation model is subject to input uncertainty caused by estimated common input models from finite data. The Input-Output Uncertainty Comparisons (IOU-C) procedure is designed to return a set of solutions that contains the best solution with an asymptotic probability guarantee when parametric input models are adopted. We extend this framework to nonparametric IOU-C (NIOU-C) when empirical distributions of the data are adopted as input models. Representing the simulation output mean of each system as a functional of the common empirical distributions via the functional Taylor series expansion, we propose two methods that rely on the nonparametric delta method and an ambiguity set formulation, respectively. We provide numerical examples to test the performance of our methods and show that they outperform the IOU-C.