On Bootstrap Iteration for Coverage Correction in Confidence Intervals
置信区间覆盖率校正中的自助法迭代AI 解读 ↓
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置信区间覆盖率校正中的自助法迭代
- 研究问题
- 迭代自助法如何改善置信区间覆盖率，以及单侧与双侧区间在覆盖误差、临界点位置和长度方面有何差异？
- 方法与思路
- 作者推导迭代后覆盖误差主导项，比较不同迭代区间，并分析覆盖校正对临界点和平均区间长度的影响。
- 材料陈述的贡献
- 摘要称，单侧与双侧区间的覆盖精度分别获得 n⁻¹ᐟ² 与 n⁻¹ 阶改善，并展示进一步校正 Bartlett 区域的例子。
- 阅读关注点
- 应核对误差阶改善的具体含义、单侧临界点二阶正确性的条件，以及覆盖改善与区间长度变化之间的关系。
- 阅读边界
- 摘要未提供渐近展开的正则条件、迭代次数和计算成本；高阶覆盖结论不能直接保证有限样本中的区间表现。
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.