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Consistency of several variants of the standardized time series area variance estimator

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  • Halim Damerdji
  • David Goldsman

Abstract

In statistical analysis of stationary time series or in steady‐state simulation output analysis, it is desired to find consistent estimates of the process variance parameter. Here, we consider variants of the area estimator of standardized time series, namely, the weighted area and the Cramér‐von Mises area estimators, and provide their consistency, in the strong sense and mean‐square sense. A sharp bound for the (asymptotic) variance of these estimators is obtained. We also present a central limit theorem for the weighted area estimator: this gives a rate of convergence of this estimator, as well as a confidence interval for the variance parameter. © 1995 John Wiley & Sons, Inc.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:42:y:1995:i:8:p:1161-1176
    DOI: 10.1002/1520-6750(199512)42:83.0.CO;2-2
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    References listed on IDEAS

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    1. Halim Damerdji, 1991. "Strong Consistency and Other Properties of the Spectral Variance Estimator," Management Science, INFORMS, vol. 37(11), pages 1424-1440, November.
    2. Peter W. Glynn & Donald L. Iglehart, 1990. "Simulation Output Analysis Using Standardized Time Series," Mathematics of Operations Research, INFORMS, vol. 15(1), pages 1-16, February.
    3. Ward Whitt, 1989. "Planning Queueing Simulations," Management Science, INFORMS, vol. 35(11), pages 1341-1366, November.
    4. Duket, Steven D. & Pritsker, A.Alan B., 1978. "Examination of simulation output using spectral methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 20(1), pages 53-60.
    5. David Goldsman & Lee Schruben, 1990. "Note---New Confidence Interval Estimators Using Standardized Time Series," Management Science, INFORMS, vol. 36(3), pages 393-397, March.
    6. Lee Schruben, 1983. "Confidence Interval Estimation Using Standardized Time Series," Operations Research, INFORMS, vol. 31(6), pages 1090-1108, December.
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    Cited by:

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    4. Kim, Hea-Jung, 2005. "A Bayesian approach to paired comparison rankings based on a graphical model," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 269-290, February.

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