An Investigation of Finite-Sample Behavior of Confidence Interval Estimators

Robert S. Sargent, Keebom Kang and David Goldsman
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Robert S. Sargent: Syracuse University, Syracuse, New York
Keebom Kang: Naval Postgraduate School, Monterey, California
David Goldsman: Georgia Institute of Technology, Atlanta, Georgia

Operations Research, 1992, vol. 40, issue 5, 898-913

Abstract: We investigate the small-sample behavior and convergence properties of confidence interval estimators (CIEs) for the mean of a stationary discrete process. We consider CIEs arising from nonoverlapping batch means, overlapping batch means, and standardized time series, all of which are commonly used in discrete-event simulation. The performance measures of interest are the coverage probability, and the expected value and variance of the half-length. We use empirical and analytical methods to make detailed comparisons regarding the behavior of the CIEs for a variety of stochastic processes. All the CIEs under study are asymptotically valid; however, they are usually invalid for small sample sizes. We find that for small samples, the bias of the variance parameter estimator figures significantly in CIE coverage performance—the less bias the better. A secondary role is played by the marginal distribution of the stationary process. We also point out that some CIEs require fewer observations before manifesting the properties for CIE validity.

Keywords: simulation; statistical analysis: batch means; overlapping batch means; standardized time series; statistics; estimation: confidence intervals on the mean; standard error; statistics; time series: confidence intervals on the mean; stationary time series (search for similar items in EconPapers)
Date: 1992
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