The estimator built by Importance Sampling method is:
is the total number of computations,
the random vectors are independent, identically distributed and following the probability density function
The asymptotic confidence interval of order associated to the estimator is
where is the quantile from the standard distribution .
This method could also be found under the name “Strategic Sampling”, “Weighted Sampling” or “Biased Sampling” (even if this estimator is not biased as it gives exactly the same result).
W.G. Cochran. Sampling Techniques. John Wiley and Sons, 1977.
M.H. Kalos et P.A. Monte Carlo Methods, volume I: Basics. John Wiley and Sons, 1986.
R.Y. Rubinstein. Simulation and the Monte Carlo Method. John Wiley and Sons, 1981.