Confidence intervals for quantiles when applying variance-reduction techniques

Document Type

Article

Publication Date

3-1-2012

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. © 2012 ACM 1049-3301/2012/03-ART10 $10.00.

Identifier

84859467885 (Scopus)

Publication Title

ACM Transactions on Modeling and Computer Simulation

External Full Text Location

https://doi.org/10.1145/2133390.2133394

e-ISSN

15581195

ISSN

10493301

Issue

2

Volume

22

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