Related papers: Quantitative deterministic equivalent of sample co…

Covariance matrix estimation, a classical statistical topic, poses significant challenges when the sample size is comparable to or smaller than the number of features. In this paper, we frame covariance matrix estimation as a compound…

A positive definite symmetric matrix {\sigma} qualifies as a quantum mechanical covariance matrix if and only if {\sigma}+(1/2)i\hbar{\Omega}\geq0 where {\Omega} is the standard symplectic matrix. This well-known condition is a strong…

In this paper, we prove the edge universality of largest eigenvalues for separable covariance matrices of the form $\mathcal Q :=A^{1/2}XBX^*A^{1/2}$. Here $X=(x_{ij})$ is an $n\times N$ random matrix with $x_{ij}=N^{-1/2}q_{ij}$, where…

In this paper, we derive new, nearly optimal bounds for the Gaussian approximation to scaled averages of $n$ independent high-dimensional centered random vectors $X_1,\dots,X_n$ over the class of rectangles in the case when the covariance…

Classical regression analysis relates the expectation of a response variable to a linear combination of explanatory variables. In this article, we propose a covariance regression model that parameterizes the covariance matrix of a…

Given finite i.i.d.~samples in a Hilbert space with zero mean and trace-class covariance operator $\Sigma$, the problem of recovering the spectral projectors of $\Sigma$ naturally arises in many applications. In this paper, we consider the…

Let the dimension $N$ of data and the sample size $T$ tend to $\infty$ with $N/T \to c > 0$. The spectral properties of a sample correlation matrix $\mathbf{C}$ and a sample covariance matrix $\mathbf{S}$ are asymptotically equal whenever…

This work is concerned with finite range bounds on the variance of individual eigenvalues of Wigner random matrices, in the bulk and at the edge of the spectrum, as well as for some intermediate eigenvalues. Relying on the GUE example,…

In the context of nonparametric regression models with one-sided errors, we consider parametric transformations of the response variable in order to obtain independence between the errors and the covariates. We focus in this paper on…

We establish a large deviation theorem for the empirical spectral distribution of random covariance matrices whose entries are independent random variables with mean 0, variance 1 and having controlled forth moments. Some new properties of…

We extend to the matrix setting a recent result of Srivastava-Vershynin about estimating the covariance matrix of a random vector. The result can be in- terpreted as a quantified version of the law of large numbers for positive…

We consider parameter inference for linear quantile regression with non-stationary predictors and errors, where the regression parameters are subject to inequality constraints. We show that the constrained quantile coefficient estimators…

The paper proves several limit theorems for linear eigenvalue statistics of overlapping Wigner and sample covariance matrices. It is shown that the covariance of the limiting multivariate Gaussian distribution is diagonalized by choosing…

Spectral correlations in unitary invariant, non-Gaussian ensembles of large random matrices possessing an eigenvalue gap are studied within the framework of the orthogonal polynomial technique. Both local and global characteristics of…

We study the minimal sample size N=N(n) that suffices to estimate the covariance matrix of an n-dimensional distribution by the sample covariance matrix in the operator norm, with an arbitrary fixed accuracy. We establish the optimal bound…

The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the `spectral estimator') for the new class of `generalized elliptical distributions' is presented. It…

Random features models play a distinguished role in the theory of deep learning, describing the behavior of neural networks close to their infinite-width limit. In this work, we present a thorough analysis of the generalization performance…

To estimate a sparse linear model from data with Gaussian noise, consilience from lasso and compressed sensing literatures is that thresholding estimators like lasso and the Dantzig selector have the ability in some situations to identify…

Consider an $n \times p$ data matrix $X$ whose rows are independently sampled from a population with covariance $\Sigma$. When $n,p$ are both large, the eigenvalues of the sample covariance matrix are substantially different from those of…

We present an alternative proof of asymptotic freeness of independent sample covariance matrices, when the dimension and the sample size grow at the same rate, by embedding these matrices into Wigner matrices of a larger order and using…