High-dimensional data arise routinely in modern statistics, econometrics, finance, genomics, and machine learning. While a large body of existing methodology is developed under Gaussian or light-tailed assumptions, many real data sets exhibit heavy tails, heterogeneity, and departures from classical covariance-based models. This book provides a systematic treatment of high-dimensional data analysis under elliptically symmetric distributions, with an emphasis on robust inference based on spatial signs, spatial ranks, multivariate Kendall's tau matrices, and related shape-based methods.The book covers the basic theory of elliptical symmetry, high-dimensional location inference, estimation and testing for covariance and precision matrices, sphericity and proportionality testing, high-dimensional alpha testing in factor pricing models, change-point analysis, white-noise and independence testing, high-dimensional discriminant analysis, and dimension reduction through principal component analysis and factor models. Throughout, we review classical low-dimensional and high-dimensional benchmark methods and then develop robust alternatives tailored to elliptical models. Particular attention is paid to the interplay between sum-type, max-type, and adaptive procedures, as well as to the role of scatter, shape, and rank-based dependence measures in heavy-tailed settings. This book is intended as a unified overview of robust high-dimensional methods under elliptical symmetry and as a synthesis of the author's recent research contributions in this area. It is written for researchers and graduate students in statistics, econometrics, and related fields who are interested in modern high-dimensional inference beyond the Gaussian paradigm.

翻译：高维数据在现代统计学、计量经济学、金融学、基因组学及机器学习中频繁出现。尽管现有大量方法学基于高斯或轻尾假设建立，但许多真实数据集呈现重尾、异质性以及偏离经典协方差模型的特征。本书系统论述了椭圆对称分布下的高维数据分析方法，重点阐述基于空间符号、空间秩、多元Kendall's tau矩阵及相关形状方法的稳健推断。内容涵盖椭圆对称基本理论、高维位置推断、协方差与精度矩阵的估计与检验、球度与比例性检验、因子定价模型中的高维alpha检验、变点分析、白噪声与独立性检验、高维判别分析，以及通过主成分分析与因子模型实现的降维。全书在回顾经典低维与高维基准方法的基础上，发展了适配椭圆模型的稳健替代方案，特别关注和型、极值型与自适应程序的相互影响，以及散度、形状和基于秩的相依度量在重尾场景中的作用。本书旨在系统综述椭圆对称框架下的稳健高维方法，并整合作者在该领域的最新研究成果，适用于统计学、计量经济学及相关领域中对超越高斯范式的高维推断感兴趣的研究人员与研究生。