Quantile Estimation Via a Combination of Conditional Monte Carlo and Randomized Quasi-Monte Carlo

Abstract

We consider the problem of estimating the p-quantile of a distribution when observations from that distribution are generated from a simulation model. The standard estimator takes the p-quantile of the empirical distribution of independent observations obtained by Monte Carlo. As an improvement, we use conditional Monte Carlo to obtain a smoother estimate of the distribution function, and we combine this with randomized quasi-Monte Carlo to further reduce the variance. The result is a much more accurate quantile estimator, whose mean square error can converge even faster than the canonical rate of O(1/n).

Variance Reduction for Generalized Likelihood Ratio Method in Quantile Sensitivity Estimation

“…We show, through simulation experiments, that the variance of the quantile sensitivity estimator by GLR can be significantly reduced by appropriately combining the method with CMC and RQMC. Similar use of CMC and RQMC for reducing the variance of quantile estimation can be found in Nakayama et al (2020).…”