Related papers: Asymptotics of eigenstructure of sample correlatio…
The aim of this paper is to establish several deep theoretical properties of principal component analysis for multiple-component spike covariance models. Our new results reveal a surprising asymptotic conical structure in critical sample…
For a large class of quantum systems the statistical properties of their spectrum show remarkable agreement with random matrix predictions. Recent advances show that the scope of random matrix theory is much wider. In this work, we show…
We consider large complex random sample covariance matrices obtained from "spiked populations", that is when the true covariance matrix is diagonal with all but finitely many eigenvalues equal to one. We investigate the limiting behavior of…
Characterizing the asymptotic distributions of eigenvectors for large random matrices poses important challenges yet can provide useful insights into a range of statistical applications. To this end, in this paper we introduce a general…
Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these…
We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the spike magnitude of leading eigenvalues, sample size, and dimensionality. This…
In this paper, we show that the largest and smallest eigenvalues of a sample correlation matrix stemming from $n$ independent observations of a $p$-dimensional time series with iid components converge almost surely to $(1+\sqrt{\gamma})^2$…
In high-dimensional principal component analysis, important inferential targets include both leading spikes and the associated principal eigenspaces. Such problems arise naturally in high-dimensional factor models, where leading principal…
Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…
In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the spiked covariance matrices, in the supercritical regime. Specifically, we derive the joint distribution of the extreme eigenvalues and the…
In this paper, we establish some new central limit theorems for certain spectral statistics of a high-dimensional sample covariance matrix under a divergent spectral norm population model. This model covers the divergent spiked population…
A common feature of high-dimensional data is that the data dimension is high, however, the sample size is relatively low. We call such data HDLSS data. In this paper, we study asymptotic properties of the first principal component in the…
In this paper, we consider a data matrix $X_N\in\mathbb{R}^{N\times p}$ where all the rows are i.i.d. samples in $\mathbb{R}^p$ of mean zero and covariance matrix $\Sigma\in\mathbb{R}^{p\times p}$. Here the population matrix $\Sigma$ is of…
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
High-dimensional autocovariance matrices play an important role in dimension reduction for high-dimensional time series. In this article, we establish the central limit theorem (CLT) for spiked eigenvalues of high-dimensional sample…
This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among…
In this article, the joint fluctuations of the extreme eigenvalues and eigenvectors of a large dimensional sample covariance matrix are analyzed when the associated population covariance matrix is a finite-rank perturbation of the identity…
Spatial-sign covariance matrix (SSCM) is an important substitute of sample covariance matrix (SCM) in robust statistics. This paper investigates the SSCM on its asymptotic spectral behaviors under high-dimensional elliptical populations,…
Suppose $\mathbf Y_n=(\mathbf y_1,\cdots,\mathbf y_n)$ is a $p\times n$ data matrix whose columns $\mathbf y_j, 1\leq j\leq n$ have different correlations. The asymptotic spectral property of $\mathbf S_n=\frac1n\mathbf Y_n\mathbf Y^*_n$…
Random correlation matrices are studied for both theoretical interestingness and importance for applications. The author of [6] is interested in their interpretation as covariance matrices of purely random signals, the authors of [16]…