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Variance of the Sample Mean: Properties and Graphs of Quadratic-Form Estimators

Author

Listed:
  • Wheyming Tina Song

    (Purdue University, West Lafayette, Indiana)

  • Bruce W. Schmeiser

    (Purdue University, West Lafayette, Indiana)

Abstract

Many commonly used estimators of the variance of the sample mean from a covariance-stationary process can be written as quadratic forms. We study the class of quadratic-form estimators algebraically and graphically, including five specific types of estimators, some from the literature and some that are new. Finite and asymptotic bias, variance, and covariance are derived and examined, with emphasis on developing intuition and insight by interpreting these properties graphically. The graphs depict the nonoptimal statistical behavior of some of the simulation literature estimators such as nonoverlapping batch means, as well as the better behavior of estimators obtained by overlapping batches.

Suggested Citation

  • Wheyming Tina Song & Bruce W. Schmeiser, 1993. "Variance of the Sample Mean: Properties and Graphs of Quadratic-Form Estimators," Operations Research, INFORMS, vol. 41(3), pages 501-517, June.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:3:p:501-517
    DOI: 10.1287/opre.41.3.501
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    Citations

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    Cited by:

    1. 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.
    2. Song, Wheyming Tina, 1996. "On the estimation of optimal batch sizes in the analysis of simulation output," European Journal of Operational Research, Elsevier, vol. 88(2), pages 304-319, January.
    3. Sarantis Tsiaplias, 2007. "A Metropolis-in-Gibbs Sampler for Estimating Equity Market Factors," Melbourne Institute Working Paper Series wp2007n18, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.
    4. Christos Alexopoulos & David Goldsman & Gamze Tokol, 2001. "Properties of Batched Quadratic-Form Variance Parameter Estimators for Simulations," INFORMS Journal on Computing, INFORMS, vol. 13(2), pages 149-156, May.
    5. Tûba Aktaran‐Kalaycı & Christos Alexopoulos & Nilay Tanık Argon & David Goldsman & James R. Wilson, 2007. "Exact expected values of variance estimators for simulation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 397-410, June.
    6. Christos Alexopoulos & Nilay Tanık Argon & David Goldsman & Gamze Tokol & James R. Wilson, 2007. "Overlapping Variance Estimators for Simulation," Operations Research, INFORMS, vol. 55(6), pages 1090-1103, December.
    7. Kin Wai Chan & Chun Yip Yau, 2017. "High-order Corrected Estimator of Asymptotic Variance with Optimal Bandwidth," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 866-898, December.

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