One-Step Bootstrapping for Smooth Iterative Procedures
针对广义最小二乘或EM算法等迭代过程，提出在每个自助法复制中只迭代一步即可获得渐近正确的估计，大幅降低计算成本，并验证了其大样本有效性和小样本适用性。
SUMMARY Resampling techniques have the potential to provide useful information about the sampling distribution of estimators of many population characteristics. Ambitious schemes such as the bootstrap and iterated bootstrap imply a substantial increase in computational effort. For some iterative procedures, such as generalized least squares or the EM algorithm, it is possible to avoid fully iterating each bootstrap replication to convergence. By analysing expansions of the defining equation, we can extract asymptotically correct bootstrap estimates from a single step for each replication. In this paper we demonstrate the large sample validity of this computationally efficient approach and illustrate its small sample applicability. Whether or not the adjustment represents an adequate replacement for full iteration depends on the nature of the problem and the desired accuracy for the bootstrap quantiles. If subsequent iterations are adjusted, then greater enhancement of the rate is achieved and the practical increase in accuracy is significant.