Folded overlapping variance estimators for simulation

We propose and analyze a new class of estimators for the variance parameter of a steady-state simulation output process. The new estimators are computed by averaging individual estimators from “folded” standardized time series based on overlapping batches composed of consecutive observations. The folding transformation on each batch can be applied more than once to produce an entire set of estimators. We establish the limiting distributions of the proposed estimators as the sample size tends to infinity while the ratio of the sample size to the batch size remains constant. We give analytical and Monte Carlo results showing that, compared to their counterparts computed from nonoverlapping batches, the new estimators have roughly the same bias but smaller variance. In addition, these estimators can be computed with order-of-sample-size work.

► We apply overlapping and folding to capture the advantages of both operations. ► FOAE have similar 1st order bias, but smaller variance than similar estimators. ► We present algorithms to get these estimators in order-of-sample-size time. ► We show the distributions of FOAE can be approximated by chi-square distributions. ► Linear combinations of level 0 and 1 FOAE an opportunity for variance reduction.