Confidence Intervals for Randomized Quasi-Monte Carlo Estimators

Pierre L'Ecuyer, Marvin K. Nakayama, Art B. Owen, Bruno Tuffin

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

Abstract

Randomized Quasi-Monte Carlo (RQMC) methods provide unbiased estimators whose variance often converges at a faster rate than standard Monte Carlo as a function of the sample size. However, computing valid confidence intervals is challenging because the observations from a single randomization are dependent and the central limit theorem does not ordinarily apply. A natural solution is to replicate the RQMC process independently a small number of times to estimate the variance and use a standard confidence interval based on a normal or Student t distribution. We investigate the standard Student t approach and two bootstrap methods for getting nonparametric confidence intervals for the mean using a modest number of replicates. Our main conclusion is that intervals based on the Student t distribution are more reliable than even the bootstrap t method on the integration problems arising from RQMC.

Original languageEnglish (US)
Title of host publication2023 Winter Simulation Conference, WSC 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages445-456
Number of pages12
ISBN (Electronic)9798350369663
DOIs
StatePublished - 2023
Event2023 Winter Simulation Conference, WSC 2023 - San Antonio, United States
Duration: Dec 10 2023Dec 13 2023

Publication series

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

Conference

Conference2023 Winter Simulation Conference, WSC 2023
Country/TerritoryUnited States
CitySan Antonio
Period12/10/2312/13/23

All Science Journal Classification (ASJC) codes

  • Software
  • Modeling and Simulation
  • Computer Science Applications

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