The accuracy of a new confidence interval method

Confidence intervals for the median of estimators or other quantiles were proposed as a substitute for usual confidence intervals in terminating and steady-state simulation. This is adequate since for many estimators the median and the expectation are close together or coincide, particularly if the sample size is large. Grouping data into batches is useful for median confidence intervals. The novel confidence intervals are easy to obtain, the variance of the estimator is not used. They are well suited for correlated simulation output data, apply to functions of estimators, and in simulation they seem to be particularly accurate, namely they follow the confidence level better than other confidence intervals. This paper states their accuracy which is the difference between the nominal confidence level and the actual coverage. The accuracy is evaluated with analytical models and simulation. For the estimation of quantiles by order statistics, the new confidence intervals are exact.