Importance Sampling and Riemann Sums
نویسنده
چکیده
The Monte Carlo method gives some estimators to evaluate the expectation E f h] based on samples from either the true density f or from some instrumental density. In this paper, we show that the Riemann sums can be coupled with the importance function. This approach produces a class of Monte Carlo estimators such that the variance is of order O(n ?2). The choice of an optimal estimator among this class is discussed. Some simulations illustrate the improvement brought by this method. Moreover, we give a criterion to assess the convergence of our "optimal" estimator to the integral of interest.
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