Optimal Linear Combinations of Overlapping Variance Estimators for Steady-State Simulation

Abstract

To estimate the variance parameter (i.e., the sum of covariances at all lags) of a steady-state simulation output process, we formulate an optimal linear combination of overlapping variance estimators (OLCOVE). Each variance estimator is computed from the same data set using one of the following methods: (i) overlapping batch means (OBM); or (ii) standardized time series (STS) applied to overlapping batches separately and then averaged over all such batches. Each estimator’s batch size is a fixed real multiple (at least unity) of a base batch size, appropriately rounded. The overall sample size is a fixed integral multiple of the base batch size. Exploiting the control-variates method, we assign OLCOVE coefficients so as to yield a minimum-variance estimator. We establish asymptotic properties of the bias and variance of OLCOVEs computed from OBM or STS variance estimators as the base batch size increases. Finally, we use OLCOVEs to construct confidence intervals for both the mean and the variance parameter of the target process. An experimental performance evaluation revealed the potential benefits of using OLCOVEs for steady-state simulation analysis.