Approximately unbiased tests of regions using multistep-multiscale bootstrap resampling
利用多步多尺度自助重抽样构造区域的近似无偏检验AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要属于一般自助法与高阶检验理论，未明确对应所列领域细分。
反馈分类问题
正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
关注这篇论文的作者
利用多步多尺度自助重抽样构造区域的近似无偏检验
- 研究问题
- 在期望参数未知的指数族中，如何针对具有光滑边界的区域零假设计算高阶准确的校正 p 值，并降低边界计算负担？
- 方法与思路
- 作者改变重抽样数据的样本量，利用样本落入区域的频率随尺度变化的信息，并引入多步多尺度程序实施几何偏差校正。
- 材料陈述的贡献
- 摘要称，新程序在指数族中给出三阶准确的 p 值，与所讨论的双重自助法及修正似然方法具有相应渐近等价关系。
- 阅读关注点
- 应核对边界光滑性、指数族条件及三阶准确性的定义，并检查多步实现、尺度选择和减少计算负担的具体依据。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；高阶结论有模型与边界条件，不能将无需模型指定的计算表述理解为任意分布下有效。
原文摘要
Approximately unbiased tests based on bootstrap probabilities are considered for the exponential family of distributions with unknown expectation parameter vector, where the null hypothesis is represented as an arbitrary-shaped region with smooth boundaries. This problem has been discussed previously in Efron and Tibshirani [Ann. Statist. 26 (1998) 1687–1718], and a corrected p-value with second-order asymptotic accuracy is calculated by the two-level bootstrap of Efron, Halloran and Holmes [Proc. Natl. Acad. Sci. U.S.A. 93 (1996) 13429–13434] based on the ABC bias correction of Efron [J. Amer. Statist. Assoc. 82 (1987) 171–185]. Our argument is an extension of their asymptotic theory, where the geometry, such as the signed distance and the curvature of the boundary, plays an important role. We give another calculation of the corrected p-value without finding the “nearest point” on the boundary to the observation, which is required in the two-level bootstrap and is an implementational burden in complicated problems. The key idea is to alter the sample size of the replicated dataset from that of the observed dataset. The frequency of the replicates falling in the region is counted for several sample sizes, and then the p-value is calculated by looking at the change in the frequencies along the changing sample sizes. This is the multiscale bootstrap of Shimodaira [Systematic Biology 51 (2002) 492–508], which is third-order accurate for the multivariate normal model. Here we introduce a newly devised multistep-multiscale bootstrap, calculating a third-order accurate p-value for the exponential family of distributions. In fact, our p-value is asymptotically equivalent to those obtained by the double bootstrap of Hall [The Bootstrap and Edgeworth Expansion (1992) Springer, New York] and the modified signed likelihood ratio of Barndorff-Nielsen [Biometrika 73 (1986) 307–322] ignoring O(n−3/2) terms, yet the computation is less demanding and free from model specification. The algorithm is remarkably simple despite complexity of the theory behind it. The differences of the p-values are illustrated in simple examples, and the accuracies of the bootstrap methods are shown in a systematic way.