Related papers: Covariance matrices of self-affine measures
We study the $k$-largest eigenvalues of heavy-tailed sample covariance matrices of the form $\bX\bX^\T$ in an asymptotic framework, where the dimension of the data and the sample size tend to infinity. To this end, we assume that the rows…
A proper set of indices characterizing the polarimetric purity of light and material media is defined from the eigenvalues of the corresponding coherency matrix. A simple and generalizable relation of these indices with the current…
A possible avenue towards the covariant formulation of the bosonic Matrix Theory is explored. The approach is guided by the known covariant description of the bosonic membrane. We point out various problems with this particular…
We study self-adjoint matrix polynomial equations in a single variable and prove existence of self-adjoint solutions under some assumptions on the leading form. Our main result is that any self-adjoint matrix polynomial equation of odd…
In this manuscript we consider random objects being measured in multiple metric spaces, which may arise when those objects may be measured in multiple distinct ways. In this new multivariate setting, we define a Fr\'echet covariance and…
We consider the problem of estimating high-dimensional covariance matrices of $K$-populations or classes in the setting where the sample sizes are comparable to the data dimension. We propose estimating each class covariance matrix as a…
The non-linear transformations incurred by the rays in an optical system can be suitably described by matrices to any desired order of approximation. In systems composed of uniform refractive index elements, each individual ray refraction…
We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
We propose a diagrammatic notation for matrix differentiation. Our new notation enables us to derive formulas for matrix differentiation more easily than the usual matrix (or index) notation. We demonstrate the effectiveness of our notation…
We derive a formula for the adjoint $\overline{A}$ of a square-matrix operation of the form $C=f(A)$, where $f$ is holomorphic in the neighborhood of each eigenvalue. We then apply the formula to derive closed-form expressions in particular…
The paper introduces a method of partial fractions with matrix coefficients and its applications to finding chains of generalized eigenvectors, to evaluation of matrix exponentials, and to solution of linear systems of ordinary differential…
We derive inclusion regions for the eigenvalues of matrix polynomials expressed in a general polynomial basis, which can lead to significantly better results than traditional bounds. We present several applications to engineering problems.
Observables in particle physics and specifically in lattice QCD calculations are often extracted from fits. Standard $\chi^2$ tests require a reliable determination of the covariance matrix and its inverse from correlated and…
We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…
Approximating significance scans of searches for new particles in high-energy physics experiments as Gaussian fields is a well-established way to estimate the trials factors required to quantify global significances. We propose a novel,…
We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in…
In multivariate time series, the estimation of the covariance matrix of the observation innovations plays an important role in forecasting as it enables the computation of the standardized forecast error vectors as well as it enables the…
This is a short proof of Ledoit-P\'ech\'e's RIE formula for covariance matrices. The proof is based on the Stein formula, which gives a very simple way to derive the result. One of the advantages of this approach is that it shows that the…
We investigate the second-order correlation function of the characteristic polynomial of a sample covariance matrix. Starting from an explicit formula for the generating function, we re-obtain several well-known kernels from random matrix…