相关论文: Spectrum estimation for large dimensional covarian…

Consider a sample of a centered random vector with unit covariance matrix. We show that under certain regularity assumptions, and up to a natural scaling, the smallest and the largest eigenvalues of the empirical covariance matrix converge,…

Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…

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…

We consider the singular vectors of any $m \times n$ submatrix of a rectangular $M \times N$ Gaussian matrix and study their asymptotic overlaps with those of the full matrix, in the macroscopic regime where $N \,/\, M\,$, $m \,/\, M$ as…

Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…

We study a class of random matrices that appear in several communication and signal processing applications, and whose asymptotic eigenvalue distribution is closely related to the reconstruction error of an irregularly sampled bandlimited…

This paper investigates limiting spectral distribution of a high-dimensional Kendall's rank correlation matrix. The underlying population is allowed to have general dependence structure. The result no longer follows the generalized…

Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…

We consider the problem of estimating a high-dimensional covariance matrix from a small number of observations when covariates on pairs of variables are available and the variables can have spatial structure. This is motivated by the…

We extend to the matrix setting a recent result of Srivastava-Vershynin about estimating the covariance matrix of a random vector. The result can be in- terpreted as a quantified version of the law of large numbers for positive…

This review article provides an overview of random matrix theory (RMT) with a focus on its growing impact on the formulation and inference of statistical models and methodologies. Emphasizing applications within high-dimensional statistics,…

Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…

We study the dependence of the spectral density of the covariance matrix ensemble on the power spectrum of the underlying multivariate signal. The white noise signal leads to the celebrated Marchenko-Pastur formula. We demonstrate results…

We study the limiting spectral distribution of large-dimensional sample covariance matrices associated with symmetric random tensors formed by $\binom{n}{d}$ different products of $d$ variables chosen from $n$ independent standardized…

In many practical situations we would like to estimate the covariance matrix of a set of variables from an insufficient amount of data. More specifically, if we have a set of $N$ independent, identically distributed measurements of an $M$…

We consider sample covariance matrices $S_N=\frac{1}{p}\Sigma_N^{1/2}X_NX_N^* \Sigma_N^{1/2}$ where $X_N$ is a $N \times p$ real or complex matrix with i.i.d. entries with finite $12^{\rm th}$ moment and $\Sigma_N$ is a $N \times N$…

This paper deals with the problem of parameter estimation based on certain eigenspaces of the empirical covariance matrix of an observed multidimensional time series, in the case where the time series dimension and the observation window…

Many statistical applications require an estimate of a covariance matrix and/or its inverse. When the matrix dimension is large compared to the sample size, which happens frequently, the sample covariance matrix is known to perform poorly…

By studying the family of $p$-dimensional scale mixtures, this paper shows for the first time a non trivial example where the eigenvalue distribution of the corresponding sample covariance matrix {\em does not converge} to the celebrated…

We study the estimation of the high-dimensional covariance matrix andits eigenvalues under dynamic volatility models. Data under such modelshave nonlinear dependency both cross-sectionally and temporally. We firstinvestigate the empirical…