Balanced Simultaneous Confidence Sets
平衡的同时置信集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：摘要研究通用同时置信集，没有足够证据对应所列经济计量细分领域。
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
平衡的同时置信集
- 研究问题
- 如何为一族参数函数选择临界值，使同时置信集达到正确的整体覆盖率，并让各个置信陈述具有相等的覆盖率？
- 方法与思路
- 作者提出一种 bootstrap 方法，联合校准各个置信集的临界值，以兼顾整体覆盖率和各组成部分的覆盖率平衡。
- 材料陈述的贡献
- 摘要称该方法在一般条件下渐近有效，涵盖正态线性模型中的经典同时区间，也可处理特征向量置信锥等问题。
- 阅读关注点
- 应核对平衡与整体覆盖率的形式化定义、bootstrap 校准步骤及渐近条件，并查看不同应用中的具体构造。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明，不能推断刊本变化；一般条件及有限样本覆盖表现未具体说明。
原文摘要
Suppose that T(θ) = {Tu (θ)} is a family of parametric functions indexed by the variable u. For each u, an approximate confidence set Cn,u for Tu (θ) may be obtained by referring a function of Tu (θ) and the sample to an estimated quantile dn,u of that function's sampling distribution. This approach is sometimes called the pivotal method for constructing a confidence set, even when it is not based on a true pivot. A simultaneous confidence set Cn for T(θ) is then obtained by simultaneously asserting the individual confidence sets {Cn,u }. The problem is to choose the critical values for the {Cn,u } in such a way that the overall coverage probability of Cn is correct and the coverage probabilities of the individual confidence sets {Cn,u } are equal. The second property is termed balance. It means that the simultaneous confidence set Cn treats each constituent confidence statement Cn,u fairly. Aside from a few special cases, the problem just described is too difficult for analytical approaches, whether exact or asymptotic in nature. A new bootstrap method described in this article, however, yields a practical solution to the problem that is asymptotically valid under general conditions. The new method recovers, as special cases, the Tukey and Scheffé simultaneous confidence intervals for the normal linear model. In addition, it handles distributionally harder problems, such as simultaneous confidence cones for the eigenvectors of an unknown covariance matrix or confidence bands for a linear predictor, in either parametric or nonparametric settings.