Nonparametric Importance Sampling
Abstract Importance sampling is a widely used variance reduction simulation technique for the evaluation of high-dimensional integrals. A key step in the implementation of importance sampling is to choose a proper distribution function from which pseudorandom numbers are generated. Parametric sampling distributions, if available at all, are often inadequate for high-dimensional integrals over irregular regions. One possible remedy is to use a nonparametric method to estimate the unknown optimal sampling function. We show that the nonparametric approach yields integral estimates that converge faster than estimates obtained from parametric approaches. We also demonstrate that an adaptive method, which has been used successfully in parametric settings, does not yield better results than simple one-step methods in the nonparametric setting.