Sequest: A sequential procedure for estimating steady-state quantiles

Abstract

Sequest is a fully sequential procedure that delivers improved point and confidence-interval (CI) estimators for a designated steady-state quantile by exploiting a combination of ideas from batching and sectioning. Sequest incorporates effective methods to do the following: (a) eliminate bias in the sectioning-based point estimator that is caused by initialization of the simulation or an inadequate simulation run length (sample size); and (b) adjust the CI half-length for the effects of skewness or correlation in the batching-based point estimators of the designated quantile. Sequest delivers a CI designed to satisfy user-specified requirements concerning both the CI's coverage probability and its absolute or relative precision. We found that Sequest exhibited good small- and large-sample properties in a preliminary evaluation of the procedure's performance on a suite of test problems that includes some problems designed to “stress test” the procedure.