  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.
