Performance of folded variance estimators for simulation

Abstract

We extend and analyze a new class of estimators for the variance parameter of a steady-state simulation output process. These estimators are based on “folded” versions of the standardized time series (STS) of the process, and are analogous to the area and Cramér--von Mises estimators calculated from the original STS. In fact, one can apply the folding mechanism more than once to produce an entire class of estimators, all of which reuse the same underlying data stream. We show that these folded estimators share many of the same properties as their nonfolded counterparts, with the added bonus that they are often nearly independent of the nonfolded versions. In particular, we derive the asymptotic distributional properties of the various estimators as the run length increases, as well as their bias, variance, and mean squared error. We also study linear combinations of these estimators, and we show that such combinations yield estimators with lower variance than their constituents. Finally, we consider the consequences of batching, and we see that the batched versions of the new estimators compare favorably to benchmark estimators such as the nonoverlapping batch means estimator.