G-2023-67
Confidence intervals for randomized quasi-Monte Carlo estimators
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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.
Published December 2023 , 11 pages
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