Discrete event simulations and parallel processing: statistical properties
SIAM Journal on Scientific and Statistical Computing
Bias properties of budget constrained simulations
Operations Research
Analysis if initial transient deletion for parallel steady-state simulations
SIAM Journal on Scientific and Statistical Computing
Adventures in stochastic processes
Adventures in stochastic processes
The asymptotic efficiency of simulation estimators
Operations Research
Regenerative steady-state simulation of discrete-event systems
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Empirical performance of bias-reducing estimators for regenerative steady-state simulations
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Nonexistence of a class of variate generation schemes
Operations Research Letters
Coupling from the past with randomized quasi-Monte Carlo
Mathematics and Computers in Simulation
Proceedings of the Winter Simulation Conference
A regenerative bootstrap approach to estimating the initial transient
Proceedings of the Winter Simulation Conference
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The time-average estimator is typically biased in the context of steady-state simulation, and its bias is of order 1/t, where t represents simulated time. Several “low-bias” estimators have been developed that have a lower order bias, and, to first-order, the same variance of the time-average. We argue that this kind of first-order comparison is insufficient, and that a second-order asymptotic expansion of the mean square error (MSE) of the estimators is needed. We provide such an expansion for the time-average estimator in both the Markov and regenerative settings. Additionally, we provide a full bias expansion and a second-order MSE expansion for the Meketon--Heidelberger low-bias estimator, and show that its MSE can be asymptotically higher or lower than that of the time-average depending on the problem. The situation is different in the context of parallel steady-state simulation, where a reduction in bias that leaves the first-order variance unaffected is arguably an improvement in performance.