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

Fang Chu; Marvin K. Nakayama

doi:10.1109/WSC.2010.5678970

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

Fang Chu, Marvin K. Nakayama

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

3 Scopus citations

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 language	English (US)
Title of host publication	Proceedings of the 2010 Winter Simulation Conference, WSC'10
Pages	2751-2761
Number of pages	11
DOIs	https://doi.org/10.1109/WSC.2010.5678970
State	Published - 2010
Event	2010 43rd Winter Simulation Conference, WSC'10 - Baltimore, MD, United States Duration: Dec 5 2010 → Dec 8 2010

Publication series

Name	Proceedings - Winter Simulation Conference
ISSN (Print)	0891-7736

Other

Other	2010 43rd Winter Simulation Conference, WSC'10
Country/Territory	United States
City	Baltimore, MD
Period	12/5/10 → 12/8/10

All Science Journal Classification (ASJC) codes

Software
Modeling and Simulation
Computer Science Applications

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10.1109/WSC.2010.5678970

Cite this

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title = "Confidence intervals for quantiles and value-at-risk when applying importance sampling",

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.",

author = "Fang Chu and Nakayama, {Marvin K.}",

year = "2010",

doi = "10.1109/WSC.2010.5678970",

language = "English (US)",

isbn = "9781424498666",

series = "Proceedings - Winter Simulation Conference",

pages = "2751--2761",

booktitle = "Proceedings of the 2010 Winter Simulation Conference, WSC'10",

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Chu, F & Nakayama, MK 2010, Confidence intervals for quantiles and value-at-risk when applying importance sampling. in Proceedings of the 2010 Winter Simulation Conference, WSC'10., 5678970, Proceedings - Winter Simulation Conference, 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

TY - GEN

T1 - Confidence intervals for quantiles and value-at-risk when applying importance sampling

AU - Chu, Fang

AU - Nakayama, Marvin K.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79951606193&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79951606193&partnerID=8YFLogxK

U2 - 10.1109/WSC.2010.5678970

DO - 10.1109/WSC.2010.5678970

M3 - Conference contribution

AN - SCOPUS:79951606193

SN - 9781424498666

T3 - Proceedings - Winter Simulation Conference

SP - 2751

EP - 2761

BT - Proceedings of the 2010 Winter Simulation Conference, WSC'10

T2 - 2010 43rd Winter Simulation Conference, WSC'10

Y2 - 5 December 2010 through 8 December 2010

ER -

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

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