Related papers: Random matrix theory and robust covariance matrix …
Around 1950, Wigner introduced the idea of modelling physical reality with an ensemble of random matrices while studying the energy levels of heavy atomic nuclei. Since then, the field of random-matrix theory has grown tremendously, with…
The Random Parameters model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we…
The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the sample covariance matrices, however, an important…
In this paper we consider ensemble of random matrices $\X_n$ with independent identically distributed vectors $(X_{ij}, X_{ji})_{i \neq j}$ of entries. Under assumption of finite fourth moment of matrix entries it is proved that empirical…
Statistical models for multivariate data often include a semi-orthogonal matrix parameter. In many applications, there is reason to expect that the semi-orthogonal matrix parameter satisfies a structural assumption such as sparsity or…
Selecting the optimal Markowitz porfolio depends on estimating the covariance matrix of the returns of $N$ assets from $T$ periods of historical data. Problematically, $N$ is typically of the same order as $T$, which makes the sample…
Although there is an extensive literature on the eigenvalues of high-dimensional sample covariance matrices, much of it is specialized to independent components (IC) models -- in which observations are represented as linear transformations…
We define a class of "algebraic" random matrices. These are random matrices for which the Stieltjes transform of the limiting eigenvalue distribution function is algebraic, i.e., it satisfies a (bivariate) polynomial equation. The Wigner…
Multivariate elliptically-contoured distributions are widely used for modeling correlated and non-Gaussian data. In this work, we study the kurtosis of the elliptical model, which is an important parameter in many statistical analysis.…
This paper is concerned with the limiting spectral behaviors of large dimensional Kendall's rank correlation matrices generated by samples with independent and continuous components. We do not require the components to be identically…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
We study modeling and inference with the Elliptical Gamma Distribution (EGD). We consider maximum likelihood (ML) estimation for EGD scatter matrices, a task for which we develop new fixed-point algorithms. Our algorithms are efficient and…
Distributional regression aims at estimating the conditional distribution of a targetvariable given explanatory co-variates. It is a crucial tool for forecasting whena precise uncertainty quantification is required. A popular methodology…
The dependency structure of multivariate data can be analyzed using the covariance matrix $\Sigma$. In many fields the precision matrix $\Sigma^{-1}$ is even more informative. As the sample covariance estimator is singular in…
Real-world signals typically span across multiple dimensions, that is, they naturally reside on multi-way data structures referred to as tensors. In contrast to standard ``flat-view'' multivariate matrix models which are agnostic to data…
We study the averaging-based distributed optimization solvers over random networks. We show a general result on the convergence of such schemes using weight-matrices that are row-stochastic almost surely and column-stochastic in expectation…
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 briefly review the random matrix theory for large N by N matrices viewed as free random variables in a context of stochastic diffusion. We establish a surprising link between the spectral properties of matrix-valued multiplicative…
The restricted maximum likelihood (REML) estimator of the dispersion matrix for random coefficient models is rewritten in terms of the sufficient statistics of the individual regressions.
A framework for quantifying dependence between random vectors is introduced. With the notion of a collapsing function, random vectors are summarized by single random variables, called collapsed random variables in the framework. Using this…