Quasi-Monte Carlo confidence intervals using quantiles of randomized nets (2504.19138v1)

Abstract: Recent advances in quasi-Monte Carlo integration have demonstrated that the median trick significantly enhances the convergence rate of linearly scrambled digital net estimators. In this work, we leverage the quantiles of such estimators to construct confidence intervals with asymptotically valid coverage for high-dimensional integrals. By analyzing the distribution of the integration error for a class of infinitely differentiable integrands, we prove that as the sample size grows, the error decomposes into an asymptotically symmetric component and a vanishing perturbation, which guarantees that a quantile-based interval for the median estimator asymptotically captures the target integral with the nominal coverage probability.