Nested simulation encompasses the estimation of functionals linked to conditional expectations through simulation techniques. In this paper, we treat conditional expectation as a function of the multidimensional conditioning variable and provide asymptotic analyses of general Least Squared Estimators on sieve, without imposing specific assumptions on the function's form. Our study explores scenarios in which the convergence rate surpasses that of the standard Monte Carlo method and the one recently proposed based on kernel ridge regression. We also delve into the conditions that allow for achieving the best possible square root convergence rate among all methods. Numerical experiments are conducted to support our statements.

翻译：嵌套模拟涉及通过模拟技术估计与条件期望相关的泛函。本文将条件期望视为多维条件变量的函数，并在不施加函数形式特定假设的情况下，对筛上一般最小二乘估计量进行渐近分析。本研究探讨了收敛速率超越标准蒙特卡洛方法及近期基于核岭回归方法的场景，同时深入分析了在所有方法中实现最优平方根收敛速率的条件。数值实验验证了我们的论断。