## Enhancing (crude method) Monte-Carlo estimator

I am currently doing a project involving Monte-Carlo method. I wonder if there is papers dealing with a "learning" refinement method to enhance the MC-convergence, example :

Objective : estimate of $E(X)\thickapprox \sum _{i=1}^{10 000}X_i$

-> step 1 (500 simulations): $approx_1=\sum _{i=1}^{500}X_i$

(i) Defining and 'Acceptance interval'

$A_1 = [approx_1-\epsilon_1,approx_1+\epsilon_1]$

where $\epsilon_1$ could be a function of the empirical variance and other statistics

-> step 2 (500 other simulations): "throwing" all simulation out of the interval $A_1$ , $approx_2=\sum _{i=1}^{500}X_i^{(2)}$

New 'acceptance interval'

$A_2 = [approx_2-\epsilon_2,approx_2+\epsilon_2]$

where $\epsilon_2 < \epsilon_1$

...

$\epsilon \xrightarrow {} 0$