Related papers: A Lanczos-Based Algorithmic Approach for Spike Det…
We provide a unified approach to a method of estimation of the regression parameter in balanced linear models with a structured covariance matrix that combines a high breakdown point and bounded influence with high asymptotic efficiency at…
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…
We obtain explicit expressions for positive integer moments of the probability density of eigenvalues of the Jacobi and Laguerre random matrix ensembles, in the asymptotic regime of large dimension. These densities are closely related to…
This paper deals with the local asymptotic structure, in the sense of Le Cam's asymptotic theory of statistical experiments, of the signal detection problem in high dimension. More precisely, we consider the problem of testing the null…
We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or…
This paper studies a method, which has been proposed in the Physics literature by [8, 7, 10], for estimating the quasi-stationary distribution. In contrast to existing methods in eigenvector estimation, the method eliminates the need for…
We investigate the complexity of covariance matrix estimation for Gibbs distributions based on dependent samples from a Markov chain. We show that when $\pi$ satisfies a Poincar\'e inequality and the chain possesses a spectral gap, we can…
We introduce a new algorithm for finding the eigenvalues and eigenvectors of Hermitian matrices within a specified region, based upon the LANSO algorithm of Parlett and Scott. It uses selective reorthogonalization to avoid the duplication…
Estimating spot covariance is an important issue to study, especially with the increasing availability of high-frequency financial data. We study the estimation of spot covariance using a kernel method for high-frequency data. In…
Covariance matrix estimation is a persistent challenge for cosmology. We focus on a class of model covariance matrices that can be generated with high accuracy and precision, using a tiny fraction of the computational resources that would…
We consider the problem of simultaneous estimation of a sequence of dependent parameters that are generated from a hidden Markov model. Based on observing a noise contaminated vector of observations from such a sequence model, we consider…
Spectral clustering is a well-known technique which identifies $k$ clusters in an undirected graph with weight matrix $W\in\mathbb{R}^{n\times n}$ by exploiting its graph Laplacian $L(W)$, whose eigenvalues $0=\lambda_1\leq \lambda_2 \leq…
This paper aims to derive asymptotical distributions of the spiked eigenvalues of the large-dimensional spiked Fisher matrices without Gaussian assumption and the restrictive assumptions on covariance matrices. We first establish invariance…
We study the spectra of MANOVA estimators for variance component covariance matrices in multivariate random effects models. When the dimensionality of the observations is large and comparable to the number of realizations of each random…
The generalized pseudospectral method is employed for the accurate calculation of eigenvalues, densities and expectation values for the spiked harmonic oscillators. This allows \emph{nonuniform} and \emph{optimal} spatial discretization of…
A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or "spike") is planted into a random matrix. These distributions form…
The present paper concerns large covariance matrix estimation via composite minimization under the assumption of low rank plus sparse structure. In this approach, the low rank plus sparse decomposition of the covariance matrix is recovered…
Advances in modern technology have enabled the simultaneous recording of neural spiking activity, which statistically can be represented by a multivariate point process. We characterise the second order structure of this process via the…
Data irregularity in cancer genomics studies has been widely observed in the form of outliers and heavy-tailed distributions in the complex traits. In the past decade, robust variable selection methods have emerged as powerful alternatives…
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,…