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


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.
Number of pages12
ISBN (Electronic)9798350369663
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


Conference2023 Winter Simulation Conference, WSC 2023
Country/TerritoryUnited States
CitySan Antonio

All Science Journal Classification (ASJC) codes

  • Software
  • Modeling and Simulation
  • Computer Science Applications


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