相关论文: Matrix Moments in a Real, Doubly Correlated Algebr…
We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…
We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for the general dimension. The formula is expressed in terms of a definite integral with…
We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…
This paper studies the problem of interacting multiple model (IMM) estimation for jump Markov linear systems with unknown measurement noise covariance. The system state and the unknown covariance are jointly estimated in the framework of…
We studied the universality of Wishart ensembles whose covariance matrix has 2 distinct eigenvalues. We studied the asymptotic limit when the number of both eigenvalues goes to infinity and obtained universality results. In this case, the…
A method for revealing the covariance matrix of an unknown two-mode Gaussian state is given based on the interference with a reference twin beam whose covariance matrix is known. In the method, first- and second-order cross-correlation…
We study the eigenvalue of the Wishart matrix, which is created from a time series with temporal correlation. When there is no correlation, the eigenvalue distribution of the Wishart matrix is known as the Marchenko-Pastur distribution…
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…
This paper develops a polynomial normal transformation model, whereby various non-normal probability distributions can be simulated by the standard normal distribution. Two methods are presented to determine the coefficients of polynomial…
Random Matrix Theory is a powerful tool in applied mathematics. Three canonical models of random matrix distributions are the Gaussian Orthogonal, Unitary and Symplectic Ensembles. For matrix ensembles defined on k-fold tensor products of…
Linear mixed models with large imbalanced crossed random effects structures pose severe computational problems for maximum likelihood estimation and for Bayesian analysis. The costs can grow as fast as $N^{3/2}$ when there are N…
We introduce and study a family of random processes with a discrete time related to products of random matrices. Such processes are formed by singular values of random matrix products, and the number of factors in a random matrix product…
This paper introduces a new Monte Carlo algorithm to invert large matrices. It is based on simultaneous coupled draws from two random vectors whose covariance is the required inverse. It can be considered a generalization of a previously…
In order to pursue the issue of the relation between the financial cross-correlations and the conventional Random Matrix Theory we analyse several characteristics of the stock market correlation matrices like the distribution of…
In finance, economics and many other fields, observations in a matrix form are often generated over time. For example, a set of key economic indicators are regularly reported in different countries every quarter. The observations at each…
High-dimensional time series has diverse applications in econometrics and finance. Recent models for capturing temporal dependence have employed a bilinear representation for matrix time series, or the Tucker-decomposition based…
A manifestly Lorentz-covariant calculus based on two matrix-coordinates and their associated derivatives is introduced. It allows formulating relativistic field theories in any even-dimensional spacetime. The construction extends a…
We consider the classical problem of estimating the covariance matrix of a subgaussian distribution from i.i.d. samples in the novel context of coarse quantization, i.e., instead of having full knowledge of the samples, they are quantized…
Generalized method of moments estimators based on higher-order moment conditions derived from independent shocks can be used to identify and estimate the simultaneous interaction in structural vector autoregressions. This study highlights…
This paper deals with the time-varying high dimensional covariance matrix estimation. We propose two covariance matrix estimators corresponding with a time-varying approximate factor model and a time-varying approximate characteristic-based…