New confidence interval estimators using standardized time series
Management Science
Properties of standardized time series weighted area variance estimators
Management Science
Optimal mean-squared-error batch sizes
Management Science
Large-sample results for batch means
Management Science
A spectral method for confidence interval generation and run length control in simulations
Communications of the ACM - Special issue on simulation modeling and statistical computing
Principles of Discrete Event Simulation
Principles of Discrete Event Simulation
Cramer-Von Mises Variance Estimators for Simulations
Operations Research
Overlapping batch means: something for nothing?
WSC '84 Proceedings of the 16th conference on Winter simulation
An Improved Batch Means Procedure for Simulation Output Analysis
Management Science
ASAP3: a batch means procedure for steady-state simulation analysis
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Introduction to Probability Models, Ninth Edition
Introduction to Probability Models, Ninth Edition
Simulation Modeling and Analysis (McGraw-Hill Series in Industrial Engineering and Management)
Simulation Modeling and Analysis (McGraw-Hill Series in Industrial Engineering and Management)
Sequential stopping rules for the regenerative method of simulation
IBM Journal of Research and Development
INFORMS Journal on Computing
Linear combinations of overlapping variance estimators for simulation
Operations Research Letters
An improved standardized time series Durbin-Watson variance estimator for steady-state simulation
Operations Research Letters
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We propose a method for estimating the variance parameter of a discrete, stationary stochastic process that involves combining variance estimators at different run lengths using linear regression. We show that the estimator thus obtained is first-order unbiased and consistent under two distinct asymptotic regimes. In the first regime, the number of constituent estimators used in the regression is fixed and the numbers of observations corresponding to the component estimators grow in a proportional manner. In the second regime, the number of constituent estimators grows while the numbers of observations corresponding to each estimator remain fixed. We also show that for m-dependent stochastic processes, one can use regression to obtain asymptotically normally distributed variance estimators in the second regime. Analytical and numerical examples indicate that the new regression-based estimators give good mean-squared-error performance in steady-state simulations. The regression methodology presented in this article can also be applied to estimate the bias of variance estimators. As an example application, we present a new sequential-stopping rule that uses the estimate for bias to determine appropriate run lengths. Monte Carlo experiments indicate that this “bias-controlling” sequential-stopping method has the potential to work well in practice.