Related papers: Simple Relative Deviation Bounds for Covariance an…
We discuss some extensions and refinements of the variance bounds for both real and complex numbers. The related bounds for the eigenvalues and spread of a matrix are also derived here.
In this paper we derive sharp lower and upper bounds for the covariance of two bounded random variables when knowledge about their expected values, variances or both is available. When only the expected values are known, our result can be…
We study sample covariance matrices arising from rectangular random matrices with i.i.d. columns. It was previously known that the resolvent of these matrices admits a deterministic equivalent when the spectral parameter stays bounded away…
We show that the empirical distribution of the eigenvalues of the sample covariance matrix of certain random vectors (not necessarily independent entries) with bounded marginal $L^{4}$ norms converges weakly to a compound free Poisson…
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…
We show that correlation matrices with particular average and variance of the correlation coefficients have a notably restricted spectral structure. Applying geometric methods, we derive lower bounds for the largest eigenvalue and the…
The goal of this paper is to obtain expectation bounds for the deviation of large sample autocovariance matrices from their means under weak data dependence. While the accuracy of covariance matrix estimation corresponding to independent…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
In this paper, we give estimates for both upper and lower bounds of eigenvalues of a simple matrix. The estimates are shaper than the known results.
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
In this paper, we derive new relative perturbation bounds for eigenvectors and eigenvalues for regular quadratic eigenvalue problems of the form $\lambda^2 M x + \lambda C x + K x = 0$, where $M$ and $K$ are nonsingular Hermitian matrices…
Estimation of covariance matrices or their inverses plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-conditioned. In this paper we present an…
This work considers the problem of estimating the distance between two covariance matrices directly from the data. Particularly, we are interested in the family of distances that can be expressed as sums of traces of functions that are…
This paper establishes sharp dimension-free concentration and expectation bounds for the deviation of a sample cross-covariance matrix from its mean. For sub-Gaussian random vectors, we prove a high-probability operator-norm bound governed…
We give two asymptotic results for the empirical distance covariance on separable metric spaces without any iid assumption on the samples. In particular, we show the almost sure convergence of the empirical distance covariance for any…
We consider a stable but nearly unstable autoregressive process of any order. The bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with spectral radius $\rho(A_{n}) < 1$ satisfying…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
This note presents sharp inequalities for deviation probability of a general quadratic form of a random vector \(\xiv\) with finite exponential moments. The obtained deviation bounds are similar to the case of a Gaussian random vector. The…
We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.
We find large deviation principles for the degree distribution and the proportion of isolated vertices for the near intermediate random geometric graph models on n vertices placed uniformly in [0, 1]^d, for d in N. In the course of the…