大维随机矩阵理论及其在高维统计中的应用

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 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 （8）CLT for Linear Spectral Statistics of LargeDimensional Sample Covariance Matrices（Z. D. Bai and Jack W. Silverstein） （9）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） （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 LargeDimensional 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 JianFeng Yao） （16）Convergence Rates to the MarchenkoPastur 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 Jianfeng 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 HighDimensional Covariance Matrices（Dandan Jiang and Zhidong Bai） （22）Partial Generalized Four Moment Theorem Revisited（Dandan Jiang and Zhidong Bai） （23）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 （24）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 （25）Limiting Spectral Distribution of a Symmetrized AutoCross 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 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 （27）Corrections to LRT on LargeDimensional Covariance Matrix by RMT（Zhidong Bai，Dandan Jiang，JianFeng Yao and Shurong Zheng） （28）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 （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 GemanHwang（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 LargeDimensional 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 HighDimensional Mean Vectors and Covariance Matrices（HU Jiang and BAI ZhiDong）