Reflected variance estimators for simulation

Abstract

We propose a new class of estimators for the asymptotic variance parameter of a stationary simulation output process. The estimators are based on Standardized Time Series (STS) functionals that converge to Brownian bridges that are themselves derived from appropriately reflected Brownian motions. The main result is that certain linear combinations of reflected estimators have substantially smaller variances than their constituents. We illustrate the performance of the new estimators via Monte Carlo experiments. These experiments show that the reflected estimators behave as expected and, in addition, perform better than certain competitors such as nonoverlapping batch means estimators and STS folded estimators.