Related papers: Eigenvector distributions and optimal shrinkage es…

This paper considers the problem of estimating the population spectral distribution from a sample covariance matrix in large dimensional situations. We generalize the contour-integral based method in Mestre (2008) and present a local moment…

We introduce a new family of estimators for unnormalized statistical models. Our family of estimators is parameterized by two nonlinear functions and uses a single sample from an auxiliary distribution, generalizing Maximum Likelihood Monte…

We study the asymptotic joint distribution of sample space--time covariance estimators of strictly stationary random fields. We do this without any marginal or joint distributional assumptions other than mild moment and mixing conditions.…

Linear discriminant analysis (LDA) is a typical method for classification problems with large dimensions and small samples. There are various types of LDA methods that are based on the different types of estimators for the covariance…

Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range…

Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…

A generalized Wigner matrix perturbed by a finite-rank deterministic matrix is considered. The fluctuations of the largest eigenvalues, which emerge outside the bulk of the spectrum, and the corresponding eigenvectors, are studied. Under…

We analyze the distribution of eigenvectors for mesoscopic, mean-field perturbations of diagonal matrices in the bulk of the spectrum. Our results apply to a generalized $N\times N$ Rosenzweig-Porter model. We prove that the eigenvectors…

We introduce kernel estimators for the semicircle law. In this first part of our general theory on the estimators, we prove the consistency and conduct simulation study to show the performance of the estimators. We also point out that…

Large-scale kernel approximation is an important problem in machine learning research. Approaches using random Fourier features have become increasingly popular [Rahimi and Recht, 2007], where kernel approximation is treated as empirical…

In this paper, we apply shrinkage strategies to estimate regression coefficients efficiently for the high-dimensional multiple regression model, where the number of samples is smaller than the number of predictors. We assume in the sparse…

We consider quasi-admissibility/inadmissibility of Stein-type shrinkage estimators of the mean of a multivariate normal distribution with covariance matrix an unknown multiple of the identity. Quasi-admissibility/inadmissibility is defined…

Correlated random fields are a common way to model dependence struc- tures in high-dimensional data, especially for data collected in imaging. One important parameter characterizing the degree of dependence is the asymp- totic variance…

This paper introduces a new method to estimate the spectral distribution of a population covariance matrix from high-dimensional data. The method is founded on a meaningful generalization of the seminal Marcenko-Pastur equation, originally…

We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…

In a recent paper, Gaunt 2020 extended Stein's method to limit distributions that can be represented as a function $g:\mathbb{R}^d\rightarrow\mathbb{R}$ of a centered multivariate normal random vector $\Sigma^{1/2}\mathbf{Z}$ with…

Let $M_n$ be a $n \times n$ Wigner or sample covariance random matrix, and let $\mu_1(M_n), \mu_2(M_n), ..., \mu_n(M_n)$ denote the unordered eigenvalues of $M_n$. We study the fluctuations of the partial linear eigenvalue statistics $$…

In this article we provide some nonnegative and positive estimators of the mean squared errors(MSEs) for shrinkage estimators of multivariate normal means. Proposed estimators are shown to improve on the uniformly minimum variance unbiased…

We use tools from random matrix theory to study the multi-spiked tensor model, i.e., a rank-$r$ deformation of a symmetric random Gaussian tensor. In particular, thanks to the nature of local optimization methods used to find the maximum…

The asymptotic efficiency of the spatial sign covariance matrix (SSCM) relative to affine equivariant estimates of scatter is studied in detail. In particular, the SSCM is shown to be asymptoticaly inadmissible, i.e. the asymptotic…