Balanced Importance Resampling for the Bootstrap

Abstract

We show that the method of importance resampling, introduced by Vernon Johns and Anthony Davison, may be enhanced by balancing the resamples. It is demonstrated that "balanced importance resampling" improves on both "balanced uniform resampling" and "random importance resampling", from the viewpoint of statistical efficiency. Moreover, the range of applications for which efficient resampling methods may be applied is extended to include statistics which are smooth functions of solutions of estimating equations.