Multivariate spacings based on data depth: I. Construction of nonparametric multivariate tolerance regions
基于数据深度的多变量间距：非参数多变量容忍区域的构造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：摘要研究一般多变量容忍区域与数据深度，未明确涉及经济分位数或分布效应。
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
基于数据深度的多变量间距：非参数多变量容忍区域的构造
- 研究问题
- 如何把一维次序统计量的间距推广到多变量数据，并构造无需预先指定形状、能够适应分布几何的容忍区域？
- 方法与思路
- 作者依数据深度建立次序统计量，将相邻深度值之间的区域定义为多变量间距，再用中心向外的层状区域构造容忍集。
- 材料陈述的贡献
- 摘要称容忍区域满足规定的内容与期望要求，并在椭圆分布下渐近最小；另提供模拟与比较研究。
- 阅读关注点
- 应核对数据深度的选择、两类容忍要求的定义、概率保证与几何适应性，以及渐近最小所采用的度量和分布条件。
- 阅读边界
- OpenAlex 摘要版本未注明；未给出深度函数和完整假设，椭圆分布下的最小性不能推广到任意分布。
原文摘要
This paper introduces and studies multivariate spacings. The spacings are developed using the order statistics derived from data depth. Specifically, the spacing between two consecutive order statistics is the region which bridges the two order statistics, in the sense that the region contains all the points whose depth values fall between the depth values of the two consecutive order statistics. These multivariate spacings can be viewed as a data-driven realization of the so-called “statistically equivalent blocks.” These spacings assume a form of center-outward layers of “shells” (“rings” in the two-dimensional case), where the shapes of the shells follow closely the underlying probabilistic geometry. The properties and applications of these spacings are studied. In particular, the spacings are used to construct tolerance regions. The construction of tolerance regions is nonparametric and completely data driven, and the resulting tolerance region reflects the true geometry of the underlying distribution. This is different from most existing approaches which require that the shape of the tolerance region be specified in advance. The proposed tolerance regions are shown to meet the prescribed specifications, in terms of β-content and β-expectation. They are also asymptotically minimal under elliptical distributions. Finally, a simulation and comparison study on the proposed tolerance regions is presented.