Randomized Quasi-Monte Carlo for Quantile Estimation

Zachary T. Kaplan, Yajuan Li, Marvin K. Nakayama, Bruno Tuffin

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

Abstract

We compare two approaches for quantile estimation via randomized quasi-Monte Carlo (RQMC) in an asymptotic setting where the number of randomizations for RQMC grows large but the size of the low-discrepancy point set remains fixed. In the first method, for each randomization, we compute an estimator of the cumulative distribution function (CDF), which is inverted to obtain a quantile estimator, and the overall quantile estimator is the sample average of the quantile estimators across randomizations. The second approach instead computes a single quantile estimator by inverting one CDF estimator across all randomizations. Because quantile estimators are generally biased, the first method leads to an estimator that does not converge to the true quantile as the number of randomizations goes to infinity. In contrast, the second estimator does, and we establish a central limit theorem for it. Numerical results further illustrate these points.

Original languageEnglish (US)
Title of host publication2019 Winter Simulation Conference, WSC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages428-439
Number of pages12
ISBN (Electronic)9781728132839
DOIs
StatePublished - Dec 2019
Event2019 Winter Simulation Conference, WSC 2019 - National Harbor, United States
Duration: Dec 8 2019Dec 11 2019

Publication series

NameProceedings - Winter Simulation Conference
Volume2019-December
ISSN (Print)0891-7736

Conference

Conference2019 Winter Simulation Conference, WSC 2019
CountryUnited States
CityNational Harbor
Period12/8/1912/11/19

All Science Journal Classification (ASJC) codes

  • Software
  • Modeling and Simulation
  • Computer Science Applications

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