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

Fang Chu, Marvin Nakayama

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

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.

Original languageEnglish (US)
Title of host publicationProceedings of the 2010 Winter Simulation Conference, WSC'10
Pages2751-2761
Number of pages11
DOIs
StatePublished - Dec 1 2010
Event2010 43rd Winter Simulation Conference, WSC'10 - Baltimore, MD, United States
Duration: Dec 5 2010Dec 8 2010

Other

Other2010 43rd Winter Simulation Conference, WSC'10
CountryUnited States
CityBaltimore, MD
Period12/5/1012/8/10

Fingerprint

Importance sampling
Value at Risk
Importance Sampling
Quantile
Confidence interval
Central limit theorem
Bahadur Representation
Estimator
Distribution functions
Invert
Point Estimate
Consistent Estimator
Cumulative distribution function
Valid
Imply
Estimate

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Science Applications
  • Modeling and Simulation

Cite this

Chu, F., & Nakayama, M. (2010). Confidence intervals for quantiles and value-at-risk when applying importance sampling. In Proceedings of the 2010 Winter Simulation Conference, WSC'10 (pp. 2751-2761). [5678970] https://doi.org/10.1109/WSC.2010.5678970
Chu, Fang ; Nakayama, Marvin. / Confidence intervals for quantiles and value-at-risk when applying importance sampling. Proceedings of the 2010 Winter Simulation Conference, WSC'10. 2010. pp. 2751-2761
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Chu, F & Nakayama, M 2010, Confidence intervals for quantiles and value-at-risk when applying importance sampling. in Proceedings of the 2010 Winter Simulation Conference, WSC'10., 5678970, pp. 2751-2761, 2010 43rd Winter Simulation Conference, WSC'10, Baltimore, MD, United States, 12/5/10. https://doi.org/10.1109/WSC.2010.5678970

Confidence intervals for quantiles and value-at-risk when applying importance sampling. / Chu, Fang; Nakayama, Marvin.

Proceedings of the 2010 Winter Simulation Conference, WSC'10. 2010. p. 2751-2761 5678970.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Chu F, Nakayama M. Confidence intervals for quantiles and value-at-risk when applying importance sampling. In Proceedings of the 2010 Winter Simulation Conference, WSC'10. 2010. p. 2751-2761. 5678970 https://doi.org/10.1109/WSC.2010.5678970