白志东,1943年生,河北省乐亭县人,教授、博士生导师,1968年毕业于中国科学技术大学数学系,1982年获博士学位。自1984年9月起,先后在美国匹兹堡大学和宾州州立大学统计系担任研究员,美国天普大学统计系担任副教授,中国台湾中山大学应用数学系和新加坡国立大学概率统计系担任教授。
1989年被评为发展中国家科学院(原第三世界科学院)院士,同时成为 International Statistics Institute Elected Member,1995年当选 Institute of Mathematical Statistics (USA) Fellow。自2002年5月回国以来,一直在东北师范大学数学与统计学院担任特聘教授。现担任 Journal of Statistical Planning and Inference 和 Statistical Papers 副主编, Random Matrices: Theory and Applications 创刊主编,曾担任中国概率统计学会常务理事,Journal of Multivariate Analysis 主编。自1982年获得博士学位后,一直从事概率统计中极限理论方面的研究,是一位多产的世界著名数学家,至今已发表学术论文近300篇。目前SCI论文引用高达4000余次,出版专著6部。
主要研究领域包括大维随机矩阵的谱分析理论、分布函数的渐近展开、模型选择、信号处理、M估计、深度估计、临床试验中的序贯设计、算法中的应用概率等。其成果在原子物理、无线电电子学、经济管理、金融保险和数理统计等方面都有重要应用。2007年获得自然科学奖一等奖,2012年获得国家自然科学奖二等奖,2022年获得四川省自然科学奖一等奖。自2016年至今,连续7年上榜爱思唯尔“中国高被引学者”。
目錄:
前言
1极限谱分布
(1)Limiting Behavior of the Eigenvalues of a Multivariate F Matrix(Y. Q. Yin,Z. D. Bai and P. R. Krishnaiah)
(2)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)
(3)Convergence to the Semicircle Law(Z. D. Bai and Y. Q. Yin)
(4)Semicircle Law for Hadamard Products(Z. D. Bai and L. X. Zhang)
(5)Large Sample Covariance Matrices Without Independence Structures in
Columns(Zhidong Bai and Wang Zhou)
(6)Convergence of the Empirical Spectral Distribution Function of Beta Matrices(Zhidong Bai,Jiang Hu,Guangming Pan and Wang Zhou)
(7)On the Semicircular Law of LargeDimensional Random Quaternion Matrices(Yanqing Yin,Zhidong Bai and Jiang Hu)
2线性谱统计量的中心极限定理
(8)CLT for Linear Spectral Statistics of LargeDimensional Sample Covariance Matrices(Z. D. Bai and Jack W. Silverstein)
(9)Substitution Principle for CLT of Linear Spectral Statistics of HighDimensional Sample Covariance Matrices with Applications to Hypothesis Testing (Shurong Zheng,Zhidong Bai and Jianfeng Yao)
(10)CLT for Linear Spectral Statistics of a Rescaled Sample Precision Matrix(Shurong Zheng,Zhidong Bai and Jianfeng Yao)
(11)CLT for Eigenvalue Statistics of LargeDimensional General Fisher Matrices with Applications(Shurong Zheng,Zhidong Bai and Jianfeng Yao)
(12)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
(13)Convergence Rate of Expected Spectral Distributions of Large Random
Matrices. Part Ⅰ. Wigner Matrices(Z. D. Bai)
(14)Convergence Rate of Expected Spectral Distributions of Large Random
Matrices. Part Ⅱ. Sample Covariance Matrices(Z. D. Bai)
(15)Convergence Rates of Spectral Distributions of Large Sample Covariance Matrices(Z. D. Bai,Baiqi Miao and JianFeng Yao)
(16)Convergence Rates to the MarchenkoPastur Type Distribution(Zhidong Bai,Jiang Hu and Wang Zhou)
4圆律
(17)Circular Law(Z. D. Bai)
5本质离群特征根的中心极限定理
(18)Central Limit Theorems for Eigenvalues in a Spiked Population Model
(Zhidong Bai and Jianfeng Yao)
(19)On Sample Eigenvalues in a Generalized Spiked Population Model(Zhidong Bai and Jianfeng Yao)
(20)Estimation of Spiked Eigenvalues in Spiked Models(Zhidong Bai and Xue Ding)
(21)Generalized Four Moment Theorem and an Application to CLT for Spiked Eigenvalues of HighDimensional Covariance Matrices(Dandan Jiang
and Zhidong Bai)
(22)Partial Generalized Four Moment Theorem Revisited(Dandan Jiang and
Zhidong Bai)
(23)Limiting Spectral Distribution of HighDimensional Noncentral Fisher Matrices and Its Analysis(Xiaozhuo Zhang,Zhidong Bai and Jiang Hu)
6非中心样本协方差矩阵
(24)No Eigenvalues Outside the Support of the Limiting Spectral Distribution of InformationPlusNoise Type Matrices(Zhidong Bai and Jack W. Silverstein)
7自协方差矩阵
(25)Limiting Spectral Distribution of a Symmetrized AutoCross Covariance Matrix(Baisuo Jin,Chen Wang,Z. D. Bai,K. Krishnan Nair and
Matthew Harding)
(26)Strong Limit of the Extreme Eigenvalues of a Symmetrized AutoCross 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
(27)Corrections to LRT on LargeDimensional Covariance Matrix by RMT(Zhidong Bai,Dandan Jiang,JianFeng Yao and Shurong Zheng)
(28)Testing the Independence of Sets of LargeDimensional Variables(JIANG DanDan,BAI ZhiDong and ZHENG ShuRong)
9特征向量的极限性质
(29)On Asymptotics of Eigenvectors of Large Sample Covariance Matrix(Z. D. Bai,B. Q. Miao and G. M. Pan)
(30)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
(31)Limiting Behavior of the Norm of Products of Random Matrices and Two Problems of GemanHwang(Z. D. Bai and Y. Q. Yin)
(32)On the Limit of the Largest Eigenvalue of the Large Dimensional Sample Covariance Matrix(Y. Q. Yin,Z. D. Bai and P. R. Krishnaiah)
(33)A Note on the Largest Eigenvalue of a Large Dimensional Sample Covariance Matrix(Z. D. Bai and Y. Q. Yin)
(34)Necessary and Sufficient Conditions for Almost Sure Convergence of
the Largest Eigenvalue of a Wigner Matrix(Z. D. Bai and Y. Q. Yin)
(35)Limit of the Smallest Eigenvalue of a Large Dimensional Sample Covariance Matrix(Z. D. Bai and Y. Q. Yin)
(36)No Eigenvalues Outside the Support of the Limiting Spectral Distribution of LargeDimensional Sample Covariance Matrices(Z. D. Bai and
Jack W. Silverstein)
(37)Exact Separation of Eigenvalues of Large Dimensional Sample Covariance Matrices(Z. D. Bai and Jack W. Silverstein)
11方法论
(38)Methodologies in Spectral Analysis of Large Dimensional Random Matrices,a Review(Z. D. Bai)
(39)Strong Representation of Weak Convergence(HU Jiang and BAI ZhiDong)
(40)A Review of 20 Years of Naive Tests of Significance for HighDimensional Mean Vectors and Covariance Matrices(HU Jiang and BAI ZhiDong)