Doubly Robust Stein-Kernelized Monte Carlo Estimator: Simultaneous Bias-Variance Reduction and Supercanonical Convergence
Doubly Robust Stein-Kernelized Monte Carlo Estimator: Simultaneous Bias-Variance Reduction and Supercanonical Convergence
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发表时间：
2021-10
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通讯作者：
H. Lam;Haofeng Zhang
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作者：
H. Lam;Haofeng Zhang
众所周知，标准蒙特卡罗计算在样本大小方面表现出典型的平方根收敛速度。最近提出了两种新的技术，一种基于控制变量，另一种基于重要性抽样，这两种技术都是从再生核和Stein恒等式的集成而来的，以减少蒙特卡罗计算中的误差到超正则收敛。本文提出了一个更通用的框架来包含这两种技术，这在样本生成器有偏差和受噪声破坏的情况下特别有用。我们展示了我们的一般估计器，我们称之为双稳健Stein核化估计器，在不同情况下的均方误差率方面优于现有的两种方法。通过数值算例验证了该方法的优越性能。
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.