相关论文: Surprising Asymptotic Conical Structure in Critica…

The classical methods of multivariate analysis are based on the eigenvalues of one or two sample covariance matrices. In many applications of these methods, for example to high dimensional data, it is natural to consider alternative…

We introduce a new approach for estimating the number of spikes in a general class of spiked covariance models without directly computing the eigenvalues of the sample covariance matrix. This approach is based on the Lanczos algorithm and…

We study one-parametric perturbations of finite dimensional real Hamiltonians depending on two controls, and we show that generically in the space of Hamiltonians, conical intersections of eigenvalues can degenerate into semi-conical…

We introduce a new random matrix model called distance covariance matrix in this paper, whose normalized trace is equivalent to the distance covariance. We first derive a deterministic limit for the eigenvalue distribution of the distance…

In this paper, we analyze the asymptotic behavior of the main characteristics of the mean-variance efficient frontier employing random matrix theory. Our particular interest covers the case when the dimension $p$ and the sample size $n$…

Motivated by dimension reduction in regression analysis and signal detection, we investigate the order determination for large dimension matrices including spiked models of which the numbers of covariates are proportional to the sample…

This paper is to study a signal-plus-noise model in high dimensional settings when the dimension and the sample size are comparable. Specifically, we assume that the noise has a general covariance matrix that allows for heteroskedasticity,…

This paper develops nonasymptotic information inequalities for the estimation of the eigenspaces of a covariance operator. These results generalize previous lower bounds for the spiked covariance model, and they show that recent upper…

We describe the spectrum of a non-self-adjoint elliptic system on a finite interval. Under certain conditions we find that the eigenvalues form a discrete set and converge asymptotically at infinity to one of several straight lines. The…

The salient properties of large empirical covariance and correlation matrices are studied for three datasets of size 54, 55 and 330. The covariance is defined as a simple cross product of the returns, with weights that decay logarithmically…

Spectral analysis of convex processes has led to many results in the analysis of differential inclusions with a convex process. In particular the characterization of eigenvalues with eigenvectors in a given cone has led to results on…

Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or…

The entropy per coordinate in a log-concave random vector of any dimension with given density at the mode is shown to have a range of just 1. Uniform distributions on convex bodies are at the lower end of this range, the distribution with…

In repeated Measure Designs with multiple groups, the primary purpose is to compare different groups in various aspects. For several reasons, the number of measurements and therefore the dimension of the observation vectors can depend on…

The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…

Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…

The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…

Localised structures appear in a wide variety of systems, arising from a pinning mechanism due to the presence of a small-scale pattern or an imposed grid. When there is a separation of lengthscales, the width of the pinning region is…

There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations -- within simple models, both are obtained from the principal eigenvector of the same…

We compute asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators for weighted sample covariances, and the joint sample-population eigenvector overlap distribution, in the spirit of Ledoit and P\'ech\'e. We…