SEQUENTIAL ESTIMATION OF STEADY-STATE QUANTILES: LESSONS LEARNED AND FUTURE DIRECTIONS

We survey recent developments concerning Sequest and Sequem, two simulation-based sequential procedures for estimating steady-state quantiles. These procedures deliver improved point and confidence-interval (CI) estimators of a selected steady-state quantile, where the CI approximately satisfies user-specified requirements on the CI's coverage probability and its absolute or relative precision. Sequest estimates a nonextreme quantile (i.e., its order is between 0.05 and 0.95) based on the methods of batching and sectioning. Sequem estimates extreme quantiles using a combination of batching, sectioning, and the maximum transformation. Two test problems show both the advantages and the limitations of these procedures. Based on the lessons learned in designing, justifying, implementing, and stress-testing Sequest and Sequem, we discuss future challenges in advancing the theory, algorithmic development, software implementation, performance evaluation, and practical application of improved procedures for steady-state quantile estimation.