  Stochastic simulation aims to compute output performance for complex models
that lack analytical tractability. To ensure accurate prediction, the model
needs to be calibrated and validated against real data. Conventional methods
approach these tasks by assessing the model-data match via simple hypothesis
tests or distance minimization in an ad hoc fashion, but they can encounter
challenges arising from non-identifiability and high dimensionality. In this
paper, we investigate a framework to develop calibration schemes that satisfy
rigorous frequentist statistical guarantees, via a basic notion that we call
eligibility set designed to bypass non-identifiability via a set-based
estimation. We investigate a feature extraction-then-aggregation approach to
construct these sets that target at multivariate outputs. We demonstrate our
methodology on several numerical examples, including an application to
calibration of a limit order book market simulator (ABIDES).
