Towards a turnkey approach for unbiased Monte Carlo estimation of smooth functions of expectations
期望的光滑函数之无偏蒙特卡洛估计：迈向自动化方法
Abstract Given a smooth function $ f $, we develop a general approach to turn Monte Carlo samples with expectation $ m $ into an unbiased estimate of $ f(m) $. Specifically, we develop estimators that are based on randomly truncating the Taylor series expansion of $ f $ and estimating the coefficients of the truncated series. We derive their properties and propose a strategy to set their tuning parameters (which depend on $ m $) automatically, with a view to making the whole…