Extremal eigenvalues of sample covariance matrices with general population

Eigenvalues of Large Sample Covariance Matrices of Spiked Population Models

We consider a spiked population model, proposed by Johnstone, whose population eigenvalues are all unit except for a few fixed eigenvalues. The question is to determine how the sample eigenvalues depend on the non-unit population ones when both sample size and population size become large. This paper completely determines the almost sure limits for a general class of samples.

Largest eigenvalues and sample covariance matrices

Exact Separation of Eigenvalues of Large Dimensional Sample Covariance Matrices

Let B n = (1/N)T 1/2 n is a Hermitian square root of the nonnegative definite Hermitian matrix T n. It is shown in Bai and Silverstein (1998) that, under certain conditions on the eigenvalues of T n , with probability one no eigenvalues lie in any interval which is outside the support of the limiting empirical distribution (known to exist) for all large n. For these n the interval corresponds t...

Extreme Eigenvalues of Sample Covariance and Correlation Matrices

This thesis is concerned with asymptotic properties of the eigenvalues of high-dimensional sample covariance and correlation matrices under an infinite fourth moment of the entries. In the first part, we study the joint distributional convergence of the largest eigenvalues of the sample covariance matrix of a p-dimensional heavy-tailed time series when p converges to infinity together with the ...

Large Deviations for Eigenvalues of Sample Covariance Matrices, with Applications to Mobile Communication Systems

We study sample covariance matrices of the form W = (1/n)CC , where C is a k × n matrix with independent and identically distributed (i.i.d.) mean 0 entries. This is a generalization of the so-calledWishart matrices, where the entries ofC are i.i.d. standard normal random variables. Such matrices arise in statistics as sample covariance matrices, and the high-dimensional case, when k is large, ...