标题： 基于随机网分位数的拟蒙特卡罗置信区间 显示英文标题

标题： Quasi-Monte Carlo confidence intervals using quantiles of randomized nets

摘要： 拟蒙特卡罗积分的最新进展表明，中值技巧显著提高了线性洗牌数字网估计量的收敛速度。 在这项工作中，我们利用此类估计量的分位数来构建具有渐近有效覆盖率的高维积分置信区间。 通过分析一类无穷可微积分函数的积分误差分布，我们证明了随着样本量的增加，误差分解为一个渐近对称的成分和一个消失的扰动，这保证了基于中位数估计量的分位数区间在名义覆盖概率下渐近捕获目标积分。 显示英文摘要

摘要： 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.