Recent advances in quasi-Monte Carlo integration demonstrate that the median of linearly scrambled digital net estimators achieves near-optimal convergence rates for high-dimensional integrals without requiring a priori knowledge of the integrand's smoothness. Building on this framework, we prove that the median estimator attains dimension-independent convergence, a property known as strong tractability in complexity theory, under tractability conditions characterized by low effective dimensionality. Using a probabilistic, integrand-specific error criterion, our analysis establishes both faster and dimension-independent convergence under weaker assumptions than previously possible in the worst-case setting.

翻译：近期拟蒙特卡洛积分的研究进展表明，线性扰动的数字网络估计量的中位数方法能够在无需被积函数光滑度先验知识的条件下，为高维积分实现近乎最优的收敛速率。在此框架基础上，我们证明了该中位数估计量在低有效维数表征的可处理性条件下，能够获得维度无关的收敛性——这一性质在复杂性理论中被称为强可处理性。通过采用基于概率的、与被积函数相关的误差准则，我们的分析证明了在比以往最坏情形设定更弱的假设条件下，该方法不仅收敛速度更快，而且具有维度无关的收敛特性。