Related papers: On eigenvalues of a high-dimensional spatial-sign …
We give an upper bound on the total variation distance between the linear eigenvalue statistic, properly scaled and centred, of a random matrix with a variance profile and the standard Gaussian random variable. The second order Poincar\'e…
This paper deals with the problem of estimating the covariance matrix of a series of independent multivariate observations, in the case where the dimension of each observation is of the same order as the number of observations. Although…
In this note, we establish an asymptotic expansion for the centering parameter appearing in the central limit theorems for linear spectral statistic of large-dimensional sample covariance matrices when the population has a spiked covariance…
Consider the sample covariance matrix $$\Sigma^{1/2}XX^T\Sigma^{1/2}$$ where $X$ is an $M\times N$ random matrix with independent entries and $\Sigma$ is an $M\times M$ diagonal matrix. It is known that if $\Sigma$ is deterministic, then…
We consider the problem of approximating the set of eigenvalues of the covariance matrix of a multivariate distribution (equivalently, the problem of approximating the "population spectrum"), given access to samples drawn from the…
Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…
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…
Consider two $p$-variate populations, not necessarily Gaussian, with covariance matrices $\Sigma_1$ and $\Sigma_2$, respectively, and let $S_1$ and $S_2$ be the sample covariances matrices from samples of the populations with degrees of…
In this paper, we use a new approach to prove that the largest eigenvalue of the sample covariance matrix of a normally distributed vector is bigger than the true largest eigenvalue with probability 1 when the dimension is infinite. We…
Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…
In this paper, we shall investigate the almost sure limits of the largest and smallest eigenvalues of a quaternion sample covariance matrix. Suppose that $\mathbf X_n$ is a $p\times n$ matrix whose elements are independent quaternion…
The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the `spectral estimator') for the new class of `generalized elliptical distributions' is presented. It…
The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultra-high dimensional setting, that is, when the dimension to sample size ratio $p/n \to \infty$. Based on this…
In this paper, we study the largest eigenvalues of sample covariance matrices with elliptically distributed data. We consider the sample covariance matrix $Q=YY^*,$ where the data matrix $Y \in \mathbb{R}^{p \times n}$ contains i.i.d.…
In this paper, we consider procedures for testing hypotheses on the dimension of the linear span generated by a growing number of $p\times p$ covariance matrices from independent $q$ populations. Under a proper limiting scheme where all the…
We introduce a class of $M \times M$ sample covariance matrices $\mathcal Q$ which subsumes and generalizes several previous models. The associated population covariance matrix $\Sigma = \mathbb E \cal Q$ is assumed to differ from the…
The properties of eigenvalues of large dimensional random matrices have received considerable attention. One important achievement is the existence and identification of the limiting spectral distribution of the empirical spectral…
We prove central limit theorem for linear eigenvalue statistics of orthogonally invariant ensembles of random matrices with one interval limiting spectrum. We consider ensembles with real analytic potentials and test functions with two…
In applied multivariate statistics, estimating the number of latent dimensions or the number of clusters, $k$, is a fundamental and recurring problem. We study a sequence of statistics called "cross-validated eigenvalues." Under a large…
We consider two classical ensembles of the random matrix theory: the Wigner matrices and sample covariance matrices, and prove Central Limit Theorem for linear eigenvalue statistics under rather weak (comparing with results known before)…