Related papers: Eigenvector distributions and optimal shrinkage es…

Efficient schemes for sampling from the eigenvalues of the Wishart distribution have recently been described for both the uncorrelated central case (where the covariance matrix is $\mathbf{I}$) and the spiked Wishart with a single spike…

This paper reviews advances in Stein-type shrinkage estimation for spherically symmetric distributions. Some emphasis is placed on developing intuition as to why shrinkage should work in location problems whether the underlying population…

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 proliferation of science and technology has led to the prevalence of voluminous data sets that are distributed across multiple machines. It is an established fact that conventional statistical methodologies may be unfeasible in the…

Stein showed that the multivariate sample mean is outperformed by "shrinking" to a constant target vector. Ledoit and Wolf extended this approach to the sample covariance matrix and proposed a multiple of the identity as shrinkage target.…

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…

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…

Tyler's and Maronna's M-estimators, as well as their regularized variants, are popular robust methods to estimate the scatter or covariance matrix of a multivariate distribution. In this work, we study the non-asymptotic behavior of these…

This work addresses large dimensional covariance matrix estimation with unknown mean. The empirical covariance estimator fails when dimension and number of samples are proportional and tend to infinity, settings known as Kolmogorov…

In this paper, we study the convergent limits and rates of the eigenvalues and eigenvectors for spiked sample covariance matrices whose spectrum can have multiple bulk components. Our model is an extension of Johnstone's spiked covariance…

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 $N \times N$…

The problem of estimating a normal covariance matrix is considered from a decision-theoretic point of view, where the dimension of the covariance matrix is larger than the sample size. This paper addresses not only the nonsingular case but…

We study shrinkage estimation of the mean parameters of a class of multivariate distributions for which the diagonal entries of the corresponding covariance matrix are certain quadratic functions of the mean parameter. This class of…

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…

Modern datasets are trending towards ever higher dimension. In response, recent theoretical studies of covariance estimation often assume the proportional-growth asymptotic framework, where the sample size $n$ and dimension $p$ are…

One of the major challenges in multivariate analysis is the estimation of population covariance matrix from sample covariance matrix (SCM). Most recent covariance matrix estimators use either shrinkage transformations or asymptotic results…

When shrinking a covariance matrix towards (a multiple) of the identity matrix, the trace of the covariance matrix arises naturally as the optimal scaling factor for the identity target. The trace also appears in other context, for example…

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…

This article provides a central limit theorem for a consistent estimator of population eigenvalues with large multiplicities based on sample covariance matrices. The focus is on limited sample size situations, whereby the number of…

Let \{$X_{ij}$\}, $i,j=...,$ be a double array of i.i.d. complex random variables with $EX_{11}=0,E|X_{11}|^2=1$ and $E|X_{11}|^4<\infty$, and let $A_n=\frac{1}{N}T_n^{{1}/{2}}X_nX_n^*T_n^{{1}/{2}}$, where $T_n^{{1}/{2}}$ is the square root…