Abstract: An approach combining saddlepoint approximation and importance resampling is developed for approximating the bootstrap distribution of a statistic which is a smooth function of sample means. The idea is to approximate the distribution of the linear part of the statistic, say Y 0, by the saddlepoint technique and then to correct the approximation by the conditional expectation of the quadratic part of the statistic, say Y1, given Y0, where the conditional expectation is to be approximated by importance resampling. Techniques for simulating the conditional expectation are developed. The approach is compared with the smoothed importance resampling method through examples. It turns out that, with negligible extra work, significant efficiency gains can be achieved over importance resampling by use of our approach.
Key words and phrases: Bootstrap, conditional expectation, distribution function estimation, importance resampling, saddlepoint approximation.