Sequential Estimation of Steady-State Quantiles: Some New Developments in Methods and Software

Recent developments are summarized concerning Sequest and Sequem, sequential procedures for estimating nonextreme and extreme steady-state quantiles of a simulation output process. The procedures deliver point and confidence-interval (CI) estimators of a given quantile, where each CI approximately satisfies given requirements on its coverage probability and its absolute or relative precision. The public-domain Sequest software now includes both procedures. The software is applied to a user-supplied dataset exhibiting warm-up effects, autocorrelation, and a multimodal marginal distribution. For the simulation analysis method of standardized time series (STS), we also sketch an elementary proof of a functional central limit theorem (FCLT) that is needed to develop STS-based quantile-estimation procedures when the output process satisfies a conventional density-regularity condition and either (i) a geometric-moment contraction condition and an FCLT for a related binary process, or (ii) conventional strong-mixing conditions.