A weighted Discrepancy Bound of quasi-Monte Carlo Importance Sampling

Abstract

Importance sampling Monte-Carlo methods are widely used for the approximation of expectations with respect to partially known probability measures. In this paper we study a deterministic version of such an estimator based on quasi-Monte Carlo. We obtain an explicit error bound in terms of the star-discrepancy for this method.

14 pages, 2 figures, shorter version of the manuscript accepted for publication in Stat. Probab. Lett. (for Section 3 see online supplementary material there)