Related papers: A universal test on spikes in a high-dimensional g…

The spiked Fisher matrix is a significant topic for two-sample problems in multivariate statistical inference. This paper is dedicated to testing the number of spikes in a high-dimensional generalized spiked Fisher matrix that relaxes the…

In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). Determining the number of spikes is a fundamental problem which appears in many scientific…

In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. Especially, we…

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…

We consider general high-dimensional spiked sample covariance models and show that their leading sample spiked eigenvalues and their linear spectral statistics are asymptotically independent when the sample size and dimension are…

Although a generalized spike population model has been actively studied in random matrix theory, its application to real data has been rarely explored. We find that most methods for determining the number of spikes based on the Johnstone's…

A generalized spiked Fisher matrix is considered in this paper. We establish a criterion for the description of the support of the limiting spectral distribution of high-dimensional generalized Fisher matrix and study the almost sure limits…

This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…

This paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under a high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped…

This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…

We study the statistical decision process of detecting the low-rank signal from various signal-plus-noise type data matrices, known as the spiked random matrix models. We first show that the principal component analysis can be improved by…

This paper investigates a statistical procedure for testing the equality of two independently estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…

We study the asymptotic distributions of the spiked eigenvalues and the largest nonspiked eigenvalue of the sample covariance matrix under a general covariance matrix model with divergent spiked eigenvalues, while the other eigenvalues are…

In this paper, we investigate the asymptotic behaviors of the extreme eigenvectors in a general spiked covariance matrix, where the dimension and sample size increase proportionally. We eliminate the restrictive assumption of the block…

Random matrix theory has proven to be a valuable tool in analyzing the generalization of linear models. However, the generalization properties of even two-layer neural networks trained by gradient descent remain poorly understood. To…

We study Bayesian inference in the spiked covariance model, where a small number of spiked eigenvalues dominate the spectrum. Our goal is to infer the spiked eigenvalues, their corresponding eigenvectors, and the number of spikes, providing…

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…

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…

In this paper, we study limiting laws and consistent estimation criteria for the extreme eigenvalues in a spiked covariance model of dimension $p$. Firstly, for fixed $p$, we propose a generalized estimation criterion that can consistently…

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,…