Two-phase quantile estimation

The paper discusses the implementation of a two-phase procedure to construct confidence intervals for a simulation estimator of the steady-state quantiles of stochastic processes. We compute sample quantiles at certain grid points and use Lagrange interpolation to estimate the p quantile. The algorithm dynamically increases the sample size so that quantile estimates satisfy the proportional precision at the first phase and the relative or absolute precision at the second phase. We show that the procedure gives asymptotically unbiased quantile estimates. An experimental performance evaluation demonstrates the validity of using grid points and the quasi-independent procedure to estimate quantiles.