On Bootstrap Iteration for Coverage Correction in Confidence Intervals
通过自助法迭代校正置信区间覆盖率AI 解读 ↓
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通过自助法迭代校正置信区间覆盖率
- 研究问题
- 迭代自助法能否减少置信区间覆盖误差，单侧与双侧区间的改善有何差别，并会怎样影响临界点和区间长度？
- 方法与思路
- 作者分析覆盖率校正后的主导误差项，比较不同迭代区间，并利用渐近展开研究临界点位置与区间长度的变化。
- 材料陈述的贡献
- 摘要称单侧与双侧区间的覆盖精度改善阶数不同，并给出主导误差公式；单侧校正临界点具有二阶正确性。
- 阅读关注点
- 应核对覆盖误差阶数的确切含义、渐近展开所需条件，以及区间构造、长度变化和有限次重抽样误差的关系。
- 阅读边界
- 索引稿件版本未注明。摘要未提供正则条件或实际重抽样次数；渐近覆盖精度改善不能直接保证小样本区间更短或更准确。
原文摘要
Iterated bootstrap procedures may be used to reduce error in many statistical problems. We discuss their use in constructing confidence intervals with accurate coverage and show that bootstrap coverage correction produces improvements in coverage accuracy of order n −1/2 in one-sided intervals, but of order n −1 in two-sided intervals. Explicit formulas are provided for the dominant term in coverage error after iteration in each case. These results are used to compare various iterated bootstrap intervals and to assess the effect of bootstrap iteration on other indicators of interval performance, such as position of critical points and length of interval. We show that, for one-sided intervals, the coverage-correction algorithm yields critical points that are second-order correct. This is not the case for two-sided intervals, where second-order correctness is not crucial in obtaining high-order coverage accuracy. We also show that the asymptotic mean increase in length between the original and coverage-corrected intervals is proportional to the coverage error of the original interval. The arguments are illustrated via several examples, including the application of the bootstrap coverage-correction algorithm to reduce coverage error of Bartlett-corrected likelihood-based confidence regions from order n −2 to order n −3.