Time series: data analysis and theory
Time series: data analysis and theory
Batching methods in simulation output analysis: what we know and what we don't
WSC '96 Proceedings of the 28th conference on Winter simulation
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The purpose of this paper is to develop a nonparametric method for obtaining a confidence interval for the mean of a stationary sequence. As indicated in literature, nonparametric confidence intervals in practice often have undesirable small-sample asymmetry and coverage characteristics. These phenomena are partially due to the fact that the third and fourth cumulants of the point estimator for the stationary mean, unlike those of the standard normal random variable, are not zero. We will apply Edgeworth and Cornish-Fisher expansions theory to obtain asymptotic expansions for the errors associated with confidence intervals. The analysis isolates various elements that contribute to errors and makes it possible for us to estimate each element and hopefully correct the errors to a smaller order. We will use Glynn's method to develop first and second order correction terms for the confidence intervals. These procedures, in the meantime, also improve the asymptotic order of confidence interval accuracy.