Importance Sampling for Bootstrap Confidence Intervals
用于 Bootstrap 置信区间的重要性抽样AI 解读 ↓
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用于 Bootstrap 置信区间的重要性抽样
- 研究问题
- 构造非参数 Bootstrap 置信区间时，能否通过改变重抽样方式，提高区间端点精度并减少所需重复次数？
- 方法与思路
- 作者将重要性抽样改用于分位数估计，以指数倾斜重新居中稳健位置估计量的 Bootstrap 分布，并进行模拟比较。
- 材料陈述的贡献
- 摘要称，所列模拟提示重抽样次数可减少十倍或更多；文章还提出适用于包含对称 M 估计量的一类位置区间。
- 阅读关注点
- 应核对倾斜分布与抽样权重、渐近最优性的具体含义，以及小样本分布、学生化和计算预算对比较的影响。
- 阅读边界
- 仅据版本未注明的 OpenAlex 摘要；重复次数节省来自特定位置估计模拟，其他区间问题的可用性仅为作者展望。
原文摘要
The use of importance-sampling methods to substantially reduce the amount of resampling necessary for the construction of nonparametric bootstrap confidence intervals is investigated. The classical importance-sampling method of Hammersley and Handscomb (1964) is modified to apply to the estimation of quantiles. Based on this method, a resampling procedure is introduced that recenters the bootstrap distribution of a robust estimator of location to produce estimated confidence limits that are much more accurate (for a given amount of resampling) than those obtained by the usual bootstrap method (Efron 1982). The required recentering is accomplished with a suitable “exponential tilting” similar to that used in another connection by Field and Hampel (1982). This importance-sampling procedure is used to produce bootstrap confidence intervals for location based on a class of estimators that includes symmetric M estimators. These interval estimates are asymptotically optimal in a certain sense. Simulation results for 95% confidence intervals based on a particular robust one-step (from the median) M estimator and its studentized version are presented for sample size 20 for the normal and the normal/uniform (slash) distributions. Studentization is accomplished by dividing the location estimator by the sample analog of its asymptotic standard deviation. The importance-sampling results obtained for bootstrap replication sizes 10, 20, and 40 are compared with the standard bootstrap confidence-interval method based on 400 replications. The simulation size for each case is 10,000. These results suggest that the bootstrap replication size may be reduced by as much as a factor of 10 or more when importance sampling is used. The proposed confidence-interval procedures provide alternatives to those given by Gross (1976), Davison and Hinkley (1986), and DiCiccio and Tibshirani (1987). It seems likely that the general approach proposed in this article could be useful in a variety of other confidence-interval estimation problems.