Generating the Confidence Interval of Time Averaged Estimator Using Threshold Bootstrap

Threshold bootstrap is a modified bootstrap method that resamples data from the autocorrelated simulation outputs. The threshold bootstrap calculate the ensemble average of sample as an estimator for population mean as do other bootstrap methods. Sometimes, however, an estimator of simulation output is generated by the concept of time average such as mean queue size in queueing system. In this situation, to analyze the simulation output more efficiently, we introduce a method of generating the confidence intervals for time averaged estimators using the threshold bootstrap. Numerical examples are provided to verify the confidence interval produced by our method.