Importance sampling for stochastic simulations
Management Science
Control variates for quantile estimation
Management Science
Control Variates for Probability and Quantile Estimation
Management Science
Variance Reduction Techniques for Estimating Value-at-Risk
Management Science
Probabilistic Error Bounds for Simulation Quantile Estimators
Management Science
Asymptotics and fast simulation for tail probabilities of maximum of sums of few random variables
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Confidence intervals for quantiles when applying variance-reduction techniques
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Operations Research Letters
Asymptotic properties of kernel density estimators when applying importance sampling
Proceedings of the Winter Simulation Conference
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Quantiles, which are known as values-at-risk in finance, are often used to measure risk. Confidence intervals provide a way of assessing the error of quantile estimators. When estimating extreme quantiles using crude Monte Carlo, the confidence intervals may have large half-widths, thus motivating the use of variance-reduction techniques (VRTs). This paper develops methods for constructing confidence intervals for quantiles when applying the VRT importance sampling. The confidence intervals, which are asymptotically valid as the number of samples grows large, are based on a technique known as sectioning. Empirical results seem to indicate that sectioning can lead to confidence intervals having better coverage than other existing methods.