On Importance Resampling for the Bootstrap
提出一种无需解析计算概率的经验重要性重抽样方法，可用于自助法置信区间和假设检验的蒙特卡洛计算，并证明最优重要性重抽样在估计偏差、方差等时无法优于均匀重抽样。
We introduce an empirical method of importance resampling, which does not require analytical calculation of the resampling probabilities. Our method can easily be used as part of a general algorithm for Monte Carlo calculation of bootstrap confidence intervals and hypothesis tests. It produces consistent, efficient and unbiased Monte Carlo approximations. We also present a very general but elementary account of importance resampling, which shows that even optimal importance resampling cannot improve on uniform resampling for calculating bootstrap estimates of bias, variance, skewness and related quantities. This result demonstrates a major difference between importance resampling and other approaches to efficient bootstrap simulation, such as balanced resampling and antithetic resampling, which produce significant improvements in efficiency for a wide range of problems involving the bootstrap.