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Skart: A skewness- and autoregression-adjusted batch-means procedure for simulation analysis

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  • Ali Tafazzoli
  • James Wilson

Abstract

Skart is an automated sequential batch-means procedure for constructing a skewness- and autoregression-adjusted confidence interval (CI) for the steady-state mean of a simulation output process either in discrete time (i.e., using observation-based statistics), or in continuous time (i.e., using time-persistent statistics). Skart delivers a CI designed to satisfy user-specified requirements concerning both the CI's coverage probability and its absolute or relative precision. Skart exploits separate adjustments to the classical batch-means CI to account for the effects on the distribution of the underlying Student's t-statistic arising from skewness and autocorrelation of the batch means. The skewness adjustment is based on a Cornish–Fisher expansion for the classical batch-means t-statistic, and the autocorrelation adjustment is based on a first-order autoregressive approximation to the batch-means autocorrelation function. Skart also delivers a point estimator for the steady-state mean that is approximately free of initialization bias. The associated warm-up period is based on iteratively applying Von Neumann's randomness test to spaced batch means with increasing sizes for each batch and its preceding spacer. In extensive experimentation, Skart compared favorably with its competitors. [Supplementary material is available for this article. Go to the publisher's online edition of IIE Transactions for additional discussion, detailed proofs, etc.]

Suggested Citation

  • Ali Tafazzoli & James Wilson, 2011. "Skart: A skewness- and autoregression-adjusted batch-means procedure for simulation analysis," IISE Transactions, Taylor & Francis Journals, vol. 43(2), pages 110-128.
  • Handle: RePEc:taf:uiiexx:v:43:y:2011:i:2:p:110-128
    DOI: 10.1080/0740817X.2010.504688
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    Citations

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    Cited by:

    1. Ali Tafazzoli & James R. Wilson & Emily K. Lada & Natalie M. Steiger, 2011. "Performance of Skart: A Skewness- and Autoregression-Adjusted Batch Means Procedure for Simulation Analysis," INFORMS Journal on Computing, INFORMS, vol. 23(2), pages 297-314, May.
    2. Song-Hee Kim & Ward Whitt, 2013. "Statistical Analysis with Little's Law," Operations Research, INFORMS, vol. 61(4), pages 1030-1045, August.
    3. Yuanhui Zhang & Haipeng Wu & Brian T. Denton & James R. Wilson & Jennifer M. Lobo, 2019. "Probabilistic sensitivity analysis on Markov models with uncertain transition probabilities: an application in evaluating treatment decisions for type 2 diabetes," Health Care Management Science, Springer, vol. 22(1), pages 34-52, March.
    4. Christos Alexopoulos & David Goldsman & Anup C. Mokashi & Kai-Wen Tien & James R. Wilson, 2019. "Sequest: A Sequential Procedure for Estimating Quantiles in Steady-State Simulations," Operations Research, INFORMS, vol. 67(4), pages 1162-1183, July.
    5. Andrea Vandin & Daniele Giachini & Francesco Lamperti & Francesca Chiaromonte, 2021. "Automated and Distributed Statistical Analysis of Economic Agent-Based Models," Papers 2102.05405, arXiv.org, revised Nov 2023.
    6. Dashi I. Singham & Lee W. Schruben, 2012. "Finite-Sample Performance of Absolute Precision Stopping Rules," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 624-635, November.
    7. Andrea Vandin & Daniele Giachini & Francesco Lamperti & Francesca Chiaromonte, 2020. "Automated and Distributed Statistical Analysis of Economic Agent-Based Models," LEM Papers Series 2020/31, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.

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