Proceedings of the 35th conference on Winter simulation: driving innovation
Some large deviations results for Latin hypercube sampling
WSC '05 Proceedings of the 37th conference on Winter simulation
Estimating Quantile Sensitivities
Operations Research
Confidence intervals for quantiles when applying variance-reduction techniques
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Using sectioning to construct confidence intervals for quantiles when applying importance sampling
Proceedings of the Winter Simulation Conference
A new perspective on batched quantile estimation
Proceedings of the Winter Simulation Conference
Proceedings of the Winter Simulation Conference
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Quantile estimation has become increasingly important, particularly in the financial industry, where value at risk (VaR) has emerged as a standard measurement tool for controlling portfolio risk. In this paper, we analyze the probability that a simulation-based quantile estimator fails to lie in a prespecified neighborhood of the true quantile. First, we show that this error probability converges to zero exponentially fast with sample size for negatively dependent sampling. Then we consider stratified quantile estimators and show that the error probability for these estimators can be guaranteed to be 0 with sufficiently large, but finite, sample size. These estimators, however, require sample sizes that grow exponentially in the problem dimension. Numerical experiments on a simple VaR example illustrate the potential for variance reduction.