Virtual Statistics in Simulation via $\mathit{k}$ Nearest Neighbors

“Virtual statistics,” as we define them, are estimators of performance measures that are conditional on the occurrence of an event; virtual waiting time of a customer arriving to a queue at time ${\tau }_0$ is one example of virtual performance. In this paper, we describe a $k$-nearest-neighbor method for estimating virtual performance postsimulation from the retained sample paths, examining both its small-sample and asymptotic properties and providing two approaches for measuring the error of the $k$-nearest-neighbor estimator. We implement leave-one-replication-out cross-validation for tuning a single parameter $k$ to use for any time (or times) of interest and evaluate the prediction performance of the $k$-nearest-neighbor estimator via controlled studies. As a by-product, this paper motivates a different way of thinking about how to process the output from dynamic, discrete-event simulation.