On a Geometric Notion of Quantiles for Multivariate Data
多元数据分位数的几何定义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：摘要直接研究多元分位数及分位数回归，对应分位数与分布效应方向。
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
多元数据分位数的几何定义
- 研究问题
- 如何利用多元数据云的几何结构推广分位数，使其表达方向性的中心与极端位置，并用于多响应回归？
- 方法与思路
- 作者结合空间中位数与回归分位数的思想构造几何分位数，通过 Bahadur 型线性展开研究抽样分布，并讨论计算与离散度估计。
- 材料陈述的贡献
- 摘要称，该定义可延伸至无限维空间及多响应线性模型，并建立等变性、渐近正态性和用于置信椭球的离散度矩阵估计。
- 阅读关注点
- 阅读时应核对几何分位数的目标函数、方向参数与等变性的具体范围，以及线性展开和无限维推广各自需要的条件。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；正则条件和计算细节未说明，收敛率记号需核对原文，不能推断刊本变化。
原文摘要
An extension of the concept of quantiles in multidimensions that uses the geometry of multivariate data clouds has been considered. The approach is based on blending as well as generalization of the key ideas used in the construction of spatial median and regression quantiles, both of which have been extensively studied in the literature. These geometric quantiles are potentially useful in constructing trimmed multivariate means as well as many other L estimates of multivariate location, and they lead to a directional notion of central and extreme points in a multidimensional setup. Such quantiles can be defined as meaningful and natural objects even in infinite-dimensional Hilbert and Banach spaces, and they yield an effective generalization of quantile regression in multiresponse linear model problems. Desirable equivariance properties are shown to hold for these multivariate quantiles, and issues related to their computation for data in finite-dimensional spaces are discussed. n 1/2 consistency and asymptotic normality of sample geometric quantiles estimating the corresponding population quantiles are established after deriving a Bahadur-type linear expansion. The sampling variation of geometric quantiles is carefully investigated, and estimates for dispersion matrices, which may be used in developing confidence ellipsoids, are constructed. In course of this development of sampling distributions and related statistical properties, we observe several interesting facts, some of which are quite counterintuitive. In particular, many of the intriguing properties of spatial medians documented in the literature appear to be inherited by geometric quantiles.