Asymptotic Iterated Bootstrap Confidence Intervals
迭代 Bootstrap 置信区间的渐近近似AI 解读 ↓
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迭代 Bootstrap 置信区间的渐近近似
- 研究问题
- 迭代 Bootstrap 通常需要两层重抽样来校正覆盖水平，能否通过渐近展开减少计算，并直接近似校正量或区间端点？
- 方法与思路
- 作者提出两种渐近近似：一种以可自动化的解析计算替代第二层重抽样，另一种直接近似区间端点而无需重抽样。
- 材料陈述的贡献
- 摘要称两种方法降低迭代区间的计算需求，讨论其理论性质，并提供自动化 Fortran 实现与三个例子的模拟说明。
- 阅读关注点
- 核对适用统计量、展开阶数和正则条件，以及近似误差、实际覆盖率与计算节省之间的关系，并检查实现所需解析量。
- 阅读边界
- 所据为稿件版本未注明的 OpenAlex 索引摘要。摘要未提供覆盖误差阶或模拟数值；历史 FTP 程序的当前可用性也无法确认。
原文摘要
An iterated bootstrap confidence interval requires an additive correction to be made to the nominal coverage level of an uncorrected interval. Such correction is usually performed using a computationally intensive Monte Carlo simulation involving two nested levels of bootstrap sampling. Asymptotic expansions of the required correction and the iterated interval endpoints are used to provide two new computationally efficient methods for constructing an approximation to the iterated bootstrap confidence interval. The first asymptotic interval replaces the need for a second level of bootstrap sampling with a series of preliminary analytic calculations, which are readily automated, and from which an approximation to the coverage correction is easily obtained. The second interval directly approximates the endpoints of the iterated interval and yields, for the first time, the possibility of constructing an approximation to an iterated bootstrap confidence interval which does not require any resampling. The theoretical properties of the two intervals are considered. The computation required for their construction is detailed and has been coded in a fully automatic user-friendly Fortran program which may be obtained by anonymous ftp. A simulation study which illustrates their effectiveness on three examples is presented.