An investigation of finite-sample behavior of confidence interval estimators

The authors investigate the small-sample behavior and convergence properties of confidence interval estimators (CIEs) for the mean of a stationary discrete process. They 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. The authors 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. The authors 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. The authors also point out that some CIEs require fewer observations before manifesting the properties for CIE validity.