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.

, 11 pages

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