Quantiles, which are also known as values-at-risk in finance, frequently arise in practice as measures of risk. This article develops asymptotically valid confidence intervals for quantiles estimated via simulation using variance-reduction techniques (VRTs). We establish our results within a general framework for VRTs, which we show includes importance sampling, stratified sampling, antithetic variates, and control variates. Our method for verifying asymptotic validity is to first demonstrate that a quantile estimator obtained via a VRT within our framework satisfies a Bahadur-Ghosh representation. We then exploit this to show that the quantile estimator obeys a central limit theorem (CLT) and to develop a consistent estimator for the variance constant appearing in the CLT, which enables us to construct a confidence interval. We provide explicit formulae for the estimators for each of the VRTs considered.
|Original language||English (US)|
|Journal||ACM Transactions on Modeling and Computer Simulation|
|State||Published - Mar 1 2012|
All Science Journal Classification (ASJC) codes
- Modeling and Simulation
- Computer Science Applications