Cramér-von Mises Variance Estimators for Simulations

David Goldsman, Keebom Kang and Andrew F. Seila
Additional contact information
David Goldsman: Georgia Institute of Technology, Atlanta, Georgia
Keebom Kang: Naval Postgraduate School, Monterey, California
Andrew F. Seila: University of Georgia, Athens, Georgia

Operations Research, 1999, vol. 47, issue 2, 299-309

Abstract: We study estimators for the variance parameter σ 2 of a stationary process. The estimators are based on weighted Cramér-von Mises statistics, and certain weightings yield estimators that are “first-order unbiased” for σ 2 . We derive an expression for the asymptotic variance of the new estimators; this expression is then used to obtain the first-order unbiased estimator having the smallest variance among fixed-degree polynomial weighting functions. Our work is based on asymptotic theory; however, we present exact and empirical examples to demonstrate the new estimators' small-sample robustness. We use a single batch of observations to derive the estimators' asymptotic properties, and then we compare the new estimators among one another. In real-life applications, one would use more than one batch; we indicate how this generalization can be carried out.

Keywords: simulation; statistical analysis; statistics; estimation; time series (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:47:y:1999:i:2:p:299-309

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