  Quasi-Monte Carlo (QMC) methods are being adopted in statistical applications
due to the increasingly challenging nature of numerical integrals that are now
routinely encountered. For integrands with $d$-dimensions and derivatives of
order $\alpha$, an optimal QMC rule converges at a best-possible rate
$O(N^{-\alpha/d})$. However, in applications the value of $\alpha$ can be
unknown and/or a rate-optimal QMC rule can be unavailable. Standard practice is
to employ $\alpha_L$-optimal QMC where the lower bound $\alpha_L \leq \alpha$
is known, but in general this does not exploit the full power of QMC. One
solution is to trade-off numerical integration with functional approximation.
This strategy is explored herein and shown to be well-suited to modern
statistical computation. A challenging application to robotic arm data
demonstrates a substantial variance reduction in predictions for mechanical
torques.
