Standard Monte Carlo computation is widely known to exhibit a canonical square-root convergence speed in terms of sample size. Two recent techniques, one based on control variate and one on importance sampling, both derived from an integration of reproducing kernels and Stein's identity, have been proposed to reduce the error in Monte Carlo computation to supercanonical convergence. This paper presents a more general framework to encompass both techniques that is especially beneficial when the sample generator is biased and noise-corrupted. We show our general estimator, which we call the doubly robust Stein-kernelized estimator, outperforms both existing methods in terms of mean squared error rates across different scenarios. We also demonstrate the superior performance of our method via numerical examples.

翻译：标准蒙特卡洛计算广为人知地表现出以样本大小为基础的典型平方根收敛速度。近期，基于控制变量和重要性采样的两种技术，均源自再生核与Stein恒等式的结合，被提出以减少蒙特卡洛计算误差至超规范收敛。本文提出一个更通用的框架以涵盖这两种技术，该框架在样本生成器存在偏差且受噪声污染时尤为有益。我们证明，所提出的通用估计器——称为双重稳健Stein核化估计器——在不同场景下均优于现有方法，在均方误差率方面表现更佳。同时，通过数值示例展示了所提方法的优越性能。