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Spectral Analysis of Large Dimensional Random Matrices
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.-…
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EFFECT OF HIGH DIMENSION: BY AN EXAMPLE OF A TWO SAMPLE PROBLEM
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…
On the empirical distribution of eigenvalues of a class of large dimensional random matrices
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),…
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No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices
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…
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CLT FOR LINEAR SPECTRAL STATISTICS OF LARGE-DIMENSIONAL SAMPLE COVARIANCE MATRICES
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…
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CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data
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…
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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…
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Corrections to LRT on large-dimensional covariance matrix by RMT
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…
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Marcinkiewicz strong laws for linear statistics
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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…
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