Simulation Estimation of Quantiles from a Distribution with Known Mean

It is common in practice to estimate the quantiles of a complicated distribution by using the order statistics of a simulated sample. If the distribution of interest has known population mean, then it is often possible to improve the mean square error of the standard quantile estimator substantially through the simple device of meancorrection: subtract off the sample mean and add on the known population mean. Asymptotic results for the mean-corrected quantile estimator are derived and compared to the standard sample quantile. Simulation results for a variety of distributions and processes illustrate the asymptotic theory. Application to Markov chain Monte Carlo and to simulation-based uncertainty analysis is described.