Quasi-Monte Carlo (QMC) methods are gaining in popularity among the statistical community due to the increasingly challenging nature of numerical integrals that are routinely encountered in contemporary statistical applications. However, compared with Monte Carlo, the variance reduction literature for QMC is under-developed. This paper studies a new strategy for reducing the variance of QMC estimators called `control functionals'. We provide theoretical guarantees that demonstrate not just a constant factor variance reduction but reduced asymptotic error rates. Such methods are likely to become important with the growing adoption of QMC algorithms within emerging statistical applications.
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