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A stopping procedure based on phi-mixing conditions

The use of batch means is a well-known technique for estimating the variance of mean point estimators computed from a simulation experiment. This paper discusses implementation of a sequential procedure to determine the batch size for constructing confidence intervals for a simulation estimator of the steady-state mean of a stochastic process. Our quasi-independent (QI) procedure increases the batch size progressively until a certain number of essentially i.i.d. samples are obtained. We show that our sequential procedure gives valid confidence intervals. The only (mild) assumption is that the correlations of the stochastic process output sequence die off. An experimental performance evaluation demonstrates the validity of the QI procedure.