大维随机矩阵理论及其在高维统计中的应用

　　本书是一本汇集了作者四十年研究历程的学术论文集，共包含40篇成果丰富的论文，涵盖了11个方面的研究领域，为读者呈现一个全面而深入的学术视角。该论文集的理论层面涵盖了多种类型的随机矩阵的特征值以及特征向量不同角度的结果，精选论文内容可应用至数理统计、经济金融、信号检测等多个学科及交叉方向，希望能为各个领域的读者提供灵感。该论文集还包含了对随机矩阵领域有建设性的方法论的介绍。本书不仅是作者学术成果的总结，也是读者的一次学术盛宴。通过阅读这本论文集，读者可以深入了解到四十年来随机矩阵的发展，拓宽自己的学术视野，并从中获得新的思考和启示。无论是对有学术基础的研究人员，还是对关心随机矩阵问题的研究生来说，这本论文集都将是一本的珍贵之作。

暂缺《大维随机矩阵理论及其在高维统计中的应用》作者简介

前言
1 极限谱分布
Limiting Behavior of the Eigenvalues of a Multivariate F Matrix（Y.Q.Yin，Z.D.Bai and P.R.Krishnaiah）
On Limiting Spectral Distribution of Product of Two Random Matrices
When the Underlying Distribution Is Isotropic（Z.D.Bai，Y.Q.Yin and P.R.Krishnaiah）
Convergence to the Semicircle Law（Z.D.Bai and Y.Q.Yin）
Semicircle Law for Hadamard Products（Z.D.Bai and L.X.Zhang)
Large Sample Covariance Matrices Without Independence Structures in
Columns（Zhidong Bai and Wang Zhou)
Convergence of the Empirical Spectral Distribution Function of Beta Matrices（Zhidong Bai，Jiang Hu，Guangming Pan and Wang Zhou)
On the Semicircular Law of Large-Dimensional Random Quaternion Matrices（Yanqing Yin，Zhidong Bai and Jiang Hu)
2 线性谱统计量的中心极限定理
CLT for Linear Spectral Statistics of Large-Dimensional Sample Covariance Matrices（Z.D.Bai and Jack W.Silverstein）
Substitution Principle for CLT of Linear Spectral Statistics of High-Dimensional Sample Covariance Matrices with Applications to Hypothesis Testing （Shurong Zheng，Zhidong Bai and Jianfeng Yao）
CLT for Linear Spectral Statistics of a Rescaled Sample Precision Matrix（Shurong Zheng，Zhidong Bai and Jianfeng Yao）
CLT for Eigenvalue Statistics of Large-Dimensional General Fisher Matrices with Applications（Shurong Zheng，Zhidong Bai and Jianfeng Yao）
Central Limit Theorem for Linear Spectral Statistics of Large Dimensional Separable Sample Covariance Matrices（Zhidong Bai，Huiqin Li and
Guangming Pan）
3 经验谱分布的收敛速度
Convergence Rate of Expected Spectral Distributions of Large Random
Matrices.Part Ⅰ.Wigner Matrices（Z.D.Bai）
Convergence Rate of Expected Spectral Distributions of Large Random
Matrices.Part Ⅱ.Sample Covariance Matrices（Z.D.Bai）
Convergence Rates of Spectral Distributions of Large Sample Covariance Matrices（Z.D.Bai，Baiqi Miao and Jian-Feng Yao）
Convergence Rates to the Marchenko-Pastur Type Distribution（Zhidong Bai，Jiang Hu and Wang Zhou）
4 圆律
Circular Law（Z.D.Bai）
5 本质离群特征根的中心极限定理
Central Limit Theorems for Eigenvalues in a Spiked Population Model
（Zhidong Bai and Jian-feng Yao）
On Sample Eigenvalues in a Generalized Spiked Population Model（Zhidong Bai and Jianfeng Yao）
Estimation of Spiked Eigenvalues in Spiked Models（Zhidong Bai and Xue Ding）
Generalized Four Moment Theorem and an Application to CLT for Spiked Eigenvalues of High-Dimensional Covariance Matrices（Dandan Jiang
and Zhidong Bai）
Partial Generalized Four Moment Theorem Revisited（Dandan Jiang and
Zhidong Bai）
Limiting Spectral Distribution of High-Dimensional Noncentral Fisher Matrices and Its Analysis（Xiaozhuo Zhang，Zhidong Bai and Jiang Hu）
6 非中心样本协方差矩阵
No Eigenvalues Outside the Support of the Limiting Spectral Distribution of Information-Plus-Noise Type Matrices（Zhidong Bai and Jack W.Silverstein）
7 自协方差矩阵
Limiting Spectral Distribution of a Symmetrized Auto-Cross Covariance Matrix（Baisuo Jin，Chen Wang，Z.D.Bai，K.Krishnan Nair and
Matthew Harding）
Strong Limit of the Extreme Eigenvalues of a Symmetrized Auto-Cross Covariance Matrix（Chen Wang，Baisuo Jin，Z.D.Bai，K.Krishnan Nair and Matthew Harding）
8 随机矩阵理论在统计中的应用
Corrections to LRT on Large-Dimensional Covariance Matrix by RMT（Zhidong Bai，Dandan Jiang，Jian-Feng Yao and Shurong Zheng）
Testing the Independence of Sets of Large-Dimensional Variables（JIANG DanDan，BAI ZhiDong and ZHENG ShuRong）
9 特征向量的极限性质
On Asymptotics of Eigenvectors of Large Sample Covariance Matrix（Z.D.Bai，B.Q.Miao and G.M.Pan）
Convergence Rates of Eigenvector Empirical Spectral Distribution of Large Dimensional Sample Covariance Matrix（Ningning Xia，Yingli Qin and Zhidong Bai）
10 样本极值特征根