A finite-memory algorithm for estimating the variance of the sample mean

Abstract

Estimating the variance of the sample mean is a classical problem of steady-state simulation output analysis. Traditional batch means estimators require specification of the simulation run length a priori. To our knowledge, the Dynamic Non-overlapping Batch Means (DNBM) estimator is the only existing variance estimator that requires a constant storage space for any sample size. In this paper, we develop the Dynamic Partial-overlapping Batch Means (DPBM) algorithm, that also requires a constant storage space. In terms of the mean squared error, the statistical performance of the DPBM estimators is superior to that of the DNBM estimators.

Keywords::

• Variance of the sample mean
• batch means estimators
• mean squared error

Acknowledgements

This research is supported by the National Science Council of the Republic of China under grant NSC-95-2221-E-007-175. The author thanks David Goldsman for his comments. The author also thanks Tsu-Kuang Yang and Ming-Chang Chih for interesting discussions and help with the flowchart of the DPBM algorithm.