Strong Consistency and Other Properties of the Spectral Variance Estimator

Halim Damerdji
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Halim Damerdji: Department of Industrial Engineering, Ecole Nationale Polytechnique, El Harrach, Algiers, Algeria

Management Science, 1991, vol. 37, issue 11, 1424-1440

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.

Keywords: simulation; steady-state output analysis; spectral variance estimation; strong consistency (search for similar items in EconPapers)
Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:37:y:1991:i:11:p:1424-1440

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