Confidence intervals for quantiles and value-at-risk when applying importance sampling

Authors:
Fang Chu;Marvin K. Nakayama
Affiliations:
New Jersey Institute of Technology, Newark, NJ;New Jersey Institute of Technology, Newark, NJ
Venue:
Proceedings of the Winter Simulation Conference
Year:
2010

Citing 9
Cited 1

Importance sampling for stochastic simulations

Management Science
Control variates for quantile estimation

Management Science
Fast simulation of rare events in queueing and reliability models

ACM Transactions on Modeling and Computer Simulation (TOMACS)
Correlation-Induction Techniques for Estimating Quantiles in Simulation Experiments

Operations Research
Variance Reduction Techniques for Estimating Value-at-Risk

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)
Estimating Quantile Sensitivities

Operations Research
Conditional Monte Carlo Estimation of Quantile Sensitivities

Management Science
Asymptotic representations for importance-sampling estimators of value-at-risk and conditional value-at-risk

Operations Research Letters

Confidence intervals for quantiles when applying variance-reduction techniques

ACM Transactions on Modeling and Computer Simulation (TOMACS)

Quantified Score

Hi-index	0.00

Visualization

Abstract

We develop methods to construct asymptotically valid confidence intervals for quantiles and value-at-risk when applying importance sampling (IS). We first employ IS to estimate the cumulative distribution function (CDF), which we then invert to obtain a point estimate of the quantile. To construct confidence intervals, we show that the IS quantile estimator satisfies a Bahadur-Ghosh representation, which implies a central limit theorem (CLT) for the quantile estimator and can be used to obtain consistent estimators of the variance constant in the CLT.