Center for Risk Management Research

The normalized importance sampling estimator allows the target density f to be known only up to a multiplicative constant. We indicate how it can be derived by a delta method based approximation of a Rao-Blackwellized acceptance rejection estimator. Using additional terms in the delta method then results on a new estimator that also only requires f to be known only up to a multiplicative constant. Numerical examples indicate that the new estimator usually outperforms the normalized importance sampling estimator in terms of mean square error.