A Tutorial on Quantile Estimation via Monte Carlo

Hui Dong; Marvin K. Nakayama

doi:10.1007/978-3-030-43465-6_1

A Tutorial on Quantile Estimation via Monte Carlo

Hui Dong, Marvin K. Nakayama

Computer Science

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

7 Scopus citations

Abstract

Quantiles are frequently used to assess risk in a wide spectrum of application areas, such as finance, nuclear engineering, and service industries. This tutorial discusses Monte Carlo simulation methods for estimating a quantile, also known as a percentile or value-at-risk, where p of a distribution’s mass lies below its p-quantile. We describe a general approach that is often followed to construct quantile estimators, and show how it applies when employing naive Monte Carlo or variance-reduction techniques. We review some large-sample properties of quantile estimators. We also describe procedures for building a confidence interval for a quantile, which provides a measure of the sampling error.

Original language	English (US)
Title of host publication	Monte Carlo and Quasi-Monte Carlo Methods, MCQMC 2018
Editors	Bruno Tuffin, Pierre L’Ecuyer
Publisher	Springer
Pages	3-30
Number of pages	28
ISBN (Print)	9783030434649
DOIs	https://doi.org/10.1007/978-3-030-43465-6_1
State	Published - 2020
Event	13th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2018 - Rennes, France Duration: Jul 1 2018 → Jul 6 2018

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	324
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	13th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2018
Country/Territory	France
City	Rennes
Period	7/1/18 → 7/6/18

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Confidence intervals
Percentile
Value-at-risk
Variance-reduction techniques

Access to Document

10.1007/978-3-030-43465-6_1

Cite this

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title = "A Tutorial on Quantile Estimation via Monte Carlo",

abstract = "Quantiles are frequently used to assess risk in a wide spectrum of application areas, such as finance, nuclear engineering, and service industries. This tutorial discusses Monte Carlo simulation methods for estimating a quantile, also known as a percentile or value-at-risk, where p of a distribution{\textquoteright}s mass lies below its p-quantile. We describe a general approach that is often followed to construct quantile estimators, and show how it applies when employing naive Monte Carlo or variance-reduction techniques. We review some large-sample properties of quantile estimators. We also describe procedures for building a confidence interval for a quantile, which provides a measure of the sampling error.",

keywords = "Confidence intervals, Percentile, Value-at-risk, Variance-reduction techniques",

author = "Hui Dong and Nakayama, {Marvin K.}",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.; 13th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2018 ; Conference date: 01-07-2018 Through 06-07-2018",

year = "2020",

doi = "10.1007/978-3-030-43465-6_1",

language = "English (US)",

isbn = "9783030434649",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "3--30",

editor = "Bruno Tuffin and Pierre L{\textquoteright}Ecuyer",

booktitle = "Monte Carlo and Quasi-Monte Carlo Methods, MCQMC 2018",

}

Dong, H & Nakayama, MK 2020, A Tutorial on Quantile Estimation via Monte Carlo. in B Tuffin & P L’Ecuyer (eds), Monte Carlo and Quasi-Monte Carlo Methods, MCQMC 2018. Springer Proceedings in Mathematics and Statistics, vol. 324, Springer, pp. 3-30, 13th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2018, Rennes, France, 7/1/18. https://doi.org/10.1007/978-3-030-43465-6_1

TY - GEN

T1 - A Tutorial on Quantile Estimation via Monte Carlo

AU - Dong, Hui

AU - Nakayama, Marvin K.

PY - 2020

Y1 - 2020

N2 - Quantiles are frequently used to assess risk in a wide spectrum of application areas, such as finance, nuclear engineering, and service industries. This tutorial discusses Monte Carlo simulation methods for estimating a quantile, also known as a percentile or value-at-risk, where p of a distribution’s mass lies below its p-quantile. We describe a general approach that is often followed to construct quantile estimators, and show how it applies when employing naive Monte Carlo or variance-reduction techniques. We review some large-sample properties of quantile estimators. We also describe procedures for building a confidence interval for a quantile, which provides a measure of the sampling error.

AB - Quantiles are frequently used to assess risk in a wide spectrum of application areas, such as finance, nuclear engineering, and service industries. This tutorial discusses Monte Carlo simulation methods for estimating a quantile, also known as a percentile or value-at-risk, where p of a distribution’s mass lies below its p-quantile. We describe a general approach that is often followed to construct quantile estimators, and show how it applies when employing naive Monte Carlo or variance-reduction techniques. We review some large-sample properties of quantile estimators. We also describe procedures for building a confidence interval for a quantile, which provides a measure of the sampling error.

KW - Confidence intervals

KW - Percentile

KW - Value-at-risk

KW - Variance-reduction techniques

UR - http://www.scopus.com/inward/record.url?scp=85089427060&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85089427060&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-43465-6_1

DO - 10.1007/978-3-030-43465-6_1

M3 - Conference contribution

AN - SCOPUS:85089427060

SN - 9783030434649

T3 - Springer Proceedings in Mathematics and Statistics

SP - 3

EP - 30

BT - Monte Carlo and Quasi-Monte Carlo Methods, MCQMC 2018

A2 - Tuffin, Bruno

A2 - L’Ecuyer, Pierre

PB - Springer

T2 - 13th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2018

Y2 - 1 July 2018 through 6 July 2018

ER -

A Tutorial on Quantile Estimation via Monte Carlo

Abstract

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All Science Journal Classification (ASJC) codes

Keywords

Access to Document

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