Asymptotic Validity of Batch Means Steady-State Confidence Intervals

P. W. Glynn and E. Lim

Advancing the Frontiers of Simulation: Festschrift in Honor of George S. Fishman [David Goldsman and James R. Wilson, eds.] Springer-Verlag, New York, 87-104 (2009)

Themethod of batch means is a widely applied procedure for constructing steady-state confidence intervals. The traditional theoretical support for the method of batch means has rested on the assumption of a functional central limit theorem for the underlying process. We establish here that the method of batch means is valid for Harris recurrent Markov processes whenever the associated process satisfies a simple (non–functional) central limit theorem. This weaker condition for validity of the method of batch means is also shown to hold in the setting of one-dependent regenerative processes.