  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.
