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Spectral Analysis of Large Dimensional Random Matrices

- Z. Bai, J. W. Silverstein
- Mathematics
- 21 December 2009

Wigner Matrices and Semicircular Law.- Sample Covariance Matrices and the Mar#x010D enko-Pastur Law.- Product of Two Random Matrices.- Limits of Extreme Eigenvalues.- Spectrum Separation.-… Expand

EFFECT OF HIGH DIMENSION: BY AN EXAMPLE OF A TWO SAMPLE PROBLEM

- Z. Bai
- Mathematics
- 1999

With the rapid development of modern computing techniques, statisticians are dealing with data with much higher dimension. Consequently, due to their loss of accuracy or power, some classical… Expand

On the empirical distribution of eigenvalues of a class of large dimensional random matrices

- J. W. Silverstein, Z. Bai
- Mathematics
- 1 August 1995

A stronger result on the limiting distribution of the eigenvalues of random Hermitian matrices of the form A + XTX*, originally studied in Marcenko and Pastur, is presented. Here, X(N - n), T(n - n),… Expand

No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices

- Z. Bai, J. W. Silverstein
- Mathematics
- 1998

Let B n = (1/N)T n 1/2 X n X n *Tn 1/2 , where X n is n x N with i.i.d. complex standardized entries having finite fourth moment and T n 1/2 is a Hermitian square root of the nonnegative definite… Expand

CLT FOR LINEAR SPECTRAL STATISTICS OF LARGE-DIMENSIONAL SAMPLE COVARIANCE MATRICES

- Z. Bai, J. W. Silverstein
- Mathematics
- 1 February 2008

Let Bn = (1/N)T 1/2 n XnX∗ nT 1/2 n where Xn = (Xij ) is n × N with i.i.d. complex standardized entries having finite fourth moment, and T 1/2 n is a Hermitian square root of the nonnegative definite… Expand

CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data

- Tingting Zou, Shu-rong Zheng, Z. Bai, Jianfeng Yao, Hongtu Zhu
- MathematicsStatistical Papers
- 12 August 2017

This paper investigates the central limit theorem for linear spectral statistics of high dimensional sample covariance matrices of the form $${\mathbf {B}}_n=n^{-1}\sum _{j=1}^{n}{\mathbf… Expand

Central limit theorems for eigenvalues in a spiked population model

In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). This model is proposed by Johnstone to cope with… Expand

Corrections to LRT on large-dimensional covariance matrix by RMT

- Z. Bai, Dandan Jiang, J. Yao, Shu-rong Zheng
- Mathematics
- 3 February 2009

In this paper, we give an explanation to the failure of two likelihood ratio procedures for testing about covariance matrices from Gaussian populations when the dimension p is large compared to the… Expand

LARGE SAMPLE COVARIANCE MATRICES WITHOUT INDEPENDENCE STRUCTURES IN COLUMNS

The limiting spectral distribution of large sample covariance matrices is derived under dependence conditions. As applications, we obtain the limiting spectral distributions of Spearman's rank… Expand

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