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Inference on Eigenvalues of Wishart Distribution Using Asymptotics with respect to the Dispersion of Population Eigenvalues
eigenvalues of covariance matrix Wishart distribution test on eigenvalues interval estimation of eigenvalues
2010/4/28
In this paper we derive some new and practical results on testing and interval estimation
problems for the population eigenvalues of a Wishart matrix based on the asymptotic theory
for block-wise in...
Eigenvalues of the Laguerre Process as Non-Colliding Squared Bessel Processes
Wishart and Laguerre ensembles and processes eigenvalues as diffusions non-colliding squared Bessel processes
2009/5/4
Let A(t) be an n-times-p matrix with independent standard complex Brownian entries and set M(t)=A(t)*A(t). This is a process version of the Laguerre ensemble and as such we shall refer to it as the La...
Poisson Statistics for the Largest Eigenvalues of Wigner Random Matrices with Heavy Tails
random matrices largest eigenvalues Poisson statistics
2009/4/28
We study large Wigner random matrices in the case when the marginal distributions of matrix entries have heavy tails. We prove that the largest eigenvalues of such matrices have Poisson statistics.
Nonparametric Test for Eigenvalues of Covariance Matrix in Multipopulation
eigenvalues k-sample Mood test nonparametric test principal component score
2009/3/5
We propose a nonparametric procedure to test the hypothesis that the j-th largest eigenvalues of a covariance matrix are equal in multipopulation. We apply the Mood test by using the principal compone...
ON THE CONNECTION BETWEEN THE DISTRIBUTION OF EIGENVALUES IN MULTIPLE CORRESPONDENCE ANALYSIS AND LOG-LINEAR MODELS
Multiple Correspondence Analysis eigenvalues log-linear models graphical models normal distribution
2009/2/26
Multiple Correspondence Analysis (MCA) and log-linear modeling are two techniques for multi-way contingency table analysis having di®erent approaches and ¯elds of applications. Log-linear mod...
Inference for eigenvalues and eigenvectors of Gaussian symmetric matrices
Random matrix maximum likelihood likelihood ratio test orthogonallyinvariant submanifold curved exponential family
2010/3/17
This article presents maximum likelihood estimators (MLEs) and
log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of
Gaussian random symmetric matrices of arbitrary dimension, whe...
Universality results for largest eigenvalues of some sample covariance matrix ensembles
Universality results largest eigenvalues sample covariance matrix ensembles
2010/4/29
For sample covariance matrices with iid entries with sub-Gaussian
tails, when both the number of samples and the number of variables
become large and the ratio approaches to one, it is a well-known ...
Learning Trigonometric Polynomials from Random Samples and Exponential Inequalities for Eigenvalues of Random Matrices
eigenvalues exponential inequality learning theory randommatrix random sampling
2010/4/26
Motivated by problems arising in random sampling of trigonometric polynomials,
we derive exponential inequalities for the operator norm of the difference
between the sample second moment matrix n...