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In this paper, we give a brief review of the theory of spectral analysis of large dimensional random matrices. Most of the existing work in the literature has been stated for real matrices but the corresponding results for the complex case are also of interest, especially for researchers in Electrical and Electronic Engineering. Thus, we convert almost all… (More)

Abstract: 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 is large compared to the sample size. Next, using recent central limit theorems for linear spectral statistics of sample covariance matrices and of random F-matrices, we propose… (More)

- Z. D. Bai, Baiqi Miao, Jian-Feng Yao
- SIAM J. Matrix Analysis Applications
- 2003

In this paper, we improve known results on the convergence rates of spectral distributions of large-dimensional sample covariance matrices of size p× n. Using the Stieltjes transform, we first prove that the expected spectral distribution converges to the limiting Marčenko–Pastur distribution with the dimension sample size ratio y = yn = p/n at a rate of… (More)

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 correlation matrices, sample correlation matrices, sample covariance matrices from finite populations, and sample covariance matrices from causal AR(1) models.

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 empirical findings on various data sets. The question is to quantify the effect of the perturbation caused by the spike eigenvalues. A recent work by Baik and… (More)

- Gina M Pan, Z. D. Bai, Baoshan Miao
- 2008

Let {Xij}, i, j = . . . , be a double array of i.i.d. complex random variables with EX11 = 0,E|X11| 2 = 1 and E|X11| 4 <∞, and let An = 1 N T 1/2 n XnX ∗ nT 1/2 n , where T 1/2 n is the square root of a nonnegative definite matrix Tn and Xn is the n×N matrix of the upper-left corner of the double array. The matrix An can be considered as a sample covariance… (More)

- BY Z. D. BAI, Feifang Hu, William F Rosenberger, Z. D. Bai, Feifang Hu, William F Rosenberger
- 2001

For adaptive clinical trials using a generalized Friedman’s urn design, we derive the limiting distribution of the urn composition under staggered entry and delayed response. The stochastic delay mechanism is assumed to depend on both the treatment assigned and the patient’s response. A very general setup is employed with K treatments and L responses. When… (More)

- Ying-Chang Liang, Guangming Pan, Z. D. Bai
- IEEE Transactions on Information Theory
- 2007

Random matrix theory is used to derive the limit and asymptotic distribution of signal-to-interference-plus-noise ratio (SIR) for a class of suboptimal minimum mean-square-error (MMSE) receivers applied to large random systems with unequal-power users. We prove that the limiting SIR converges to a deterministic value when K and N go to infinity with lim K/N… (More)

- Z. D. Bai, Yan-Tsang Wu
- 1999

We consider the problem of model (or variable) selection in the classical regression model using the GIC (general information criterion). In this method the maximum likelihood is used with a penalty function denoted by Cn, depending on the sample size n and chosen to ensure consistency in the selection of the true model. There are various choices of Cn… (More)

- Z. D. Bai, L. X. Zhang
- J. Multivariate Analysis
- 2010