The Automatic Construction of Bootstrap Confidence Intervals

The standard intervals, for example, θ̂±1.96σ̂ for nominal 95% two-sided coverage, are familiar and easy to use, but can be of dubious accuracy in regular practice. Bootstrap confidence intervals offer an order of magnitude improvement—from first order to second order accuracy. This article introduces a new set of algorithms that automate the construction of bootstrap intervals, substituting computer power for the need to individually program particular applications. The algorithms are described in terms of the underlying theory that motivates them, along with examples of their application. They are implemented in the R package bcaboot. Supplementary materials for this article are available online.

常规置信区间（如标称95%双侧覆盖的θ̂±1.96σ̂）广为人知且易于使用，但在实际常规应用中其精度往往存疑。自助法置信区间(Bootstrap Confidence Intervals)可将精度提升一个数量级——从一阶精度升级至二阶精度。本文提出一组全新的自动化构建自助法置信区间的算法，以计算算力替代针对特定应用逐一编写程序的需求。本算法将基于其背后的驱动理论进行详细阐述，并附带相关应用实例。该类算法已在R语言扩展包bcaboot中实现。本文的补充材料可在线获取。