A nearest-neighbor control variates estimator gives faster integral approximation rates for random-design functional data and shorter prediction/confidence intervals in simulations, with a proved noisy-case CLT and a conjectured noiseless interval.
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Rate accelerated inference for integrals of multivariate random functions
A nearest-neighbor control variates estimator gives faster integral approximation rates for random-design functional data and shorter prediction/confidence intervals in simulations, with a proved noisy-case CLT and a conjectured noiseless interval.