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Strong Consistency and Other Properties of the Spectral Variance Estimator

Author

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  • Halim Damerdji

    (Department of Industrial Engineering, Ecole Nationale Polytechnique, El Harrach, Algiers, Algeria)

Abstract

Consistent estimation of the variance parameter of a stochastic process allows construction, under certain conditions, of a confidence interval for the mean of the process. If the variance estimator is strongly consistent, fixed-width confidence interval construction is valid for large samples. It has long been known that the spectral variance estimator of steady-state simulation output analysis is consistent in the mean-square sense. Here, we provide strong consistency of this estimator, thereby justifying fixed-width confidence interval construction for the spectral method. A characterization of spectral density function estimators is also introduced. This characterization provides insight into the relation between spectral methods and overlapping batch means-type variance estimators. Finally, some of the mathematical conditions provide qualitative insight into the relation between the process correlation and certain parameters of spectral methods.

Suggested Citation

  • Halim Damerdji, 1991. "Strong Consistency and Other Properties of the Spectral Variance Estimator," Management Science, INFORMS, vol. 37(11), pages 1424-1440, November.
    • Handle: RePEc:inm:ormnsc:v:37:y:1991:i:11:p:1424-1440
    DOI: 10.1287/mnsc.37.11.1424
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    Cited by:

    1. 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.
    2. Halim Damerdji & David Goldsman, 1995. "Consistency of several variants of the standardized time series area variance estimator," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(8), pages 1161-1176, December.
    3. Chakraborty, Saptarshi & Bhattacharya, Suman K. & Khare, Kshitij, 2022. "Estimating accuracy of the MCMC variance estimator: Asymptotic normality for batch means estimators," Statistics & Probability Letters, Elsevier, vol. 183(C).
    4. 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.
    5. Ying Liu & Dootika Vats & James M. Flegal, 2022. "Batch Size Selection for Variance Estimators in MCMC," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 65-93, March.
    6. 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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