Confidence intervals for quantiles when applying variance-reduction techniques

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Abstract

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 languageEnglish (US)
Article number10
JournalACM Transactions on Modeling and Computer Simulation
Volume22
Issue number2
DOIs
StatePublished - Mar 1 2012

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Computer Science Applications

Keywords

  • Performance
  • Theory

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