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The Song rule outperforms optimal-batch-size variance estimators in simulation output analysis

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  • Song, Wheyming Tina

Abstract

Estimating the variance of the sample mean is a fundamental problem in Monte Carlo simulation output analysis. The need is to develop a procedure to estimate this variance with minimum mean-squared-error (mse). One of the commonly used approaches is batch-means estimator (BME) including non-overlapping batch means (NBM) and overlapping batch means (OBM). The research into BMEs has pursued the elusive optimal-batch-size for many years. Another commonly used approach is to linearly combine two BMEs with large batch sizes to ignore estimating the bias constant. This paper demonstrates that such two types of pursuits are not the optimal surrogate for the minimum mse.

Suggested Citation

  • Song, Wheyming Tina, 2019. "The Song rule outperforms optimal-batch-size variance estimators in simulation output analysis," European Journal of Operational Research, Elsevier, vol. 275(3), pages 1072-1082.
    • Handle: RePEc:eee:ejores:v:275:y:2019:i:3:p:1072-1082
    DOI: 10.1016/j.ejor.2018.11.059
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    References listed on IDEAS

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    1. Tûba Aktaran-Kalaycı & Christos Alexopoulos & David Goldsman & James R. Wilson, 2009. "Optimal Linear Combinations of Overlapping Variance Estimators for Steady-State Simulation," International Series in Operations Research & Management Science, in: Christos Alexopoulos & David Goldsman & James R. Wilson (ed.), Advancing the Frontiers of Simulation, pages 291-328, Springer.
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    3. David Goldsman & Keebom Kang & Seong‐Hee Kim & Andrew F. Seila & Gamze Tokol, 2007. "Combining standardized time series area and Cramér–von Mises variance estimators," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 384-396, June.
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    9. Song, Wheyming Tina & Chih, Mingchang, 2013. "Run length not required: Optimal-mse dynamic batch means estimators for steady-state simulations," European Journal of Operational Research, Elsevier, vol. 229(1), pages 114-123.
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    Cited by:

    1. Mingchang Chih, 2019. "An Insight into the Data Structure of the Dynamic Batch Means Algorithm with Binary Tree Code," Mathematics, MDPI, vol. 7(9), pages 1-8, August.

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