相关论文: Non-Stationary Covariance Matrices And Noise

We study the dependence of the spectral density of the covariance matrix ensemble on the power spectrum of the underlying multivariate signal. The white noise signal leads to the celebrated Marchenko-Pastur formula. We demonstrate results…

We look into the fluctuations caused by disturbances in power systems. In the linearized system of the power systems, the disturbance is modeled by a Brownian motion process, and the fluctuations are described by the covariance matrix of…

We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…

Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…

Spectral properties of random matrices play an important role in statistics, machine learning, communications, and many other areas. Engaging results regarding the convergence of the empirical spectral distribution (ESD) and the…

Cooperative spectrum sensing based on the limiting eigenvalue ratio of the covariance matrix offers superior detection performance and overcomes the noise uncertainty problem. While an exact expression exists, it is complex and multiple…

We describe some numerical experiments which determine the degree of spectral instability of medium size randomly generated matrices which are far from self-adjoint. The conclusion is that the eigenvalues are likely to be intrinsically…

In many astrophysical settings covariance matrices of large datasets have to be determined empirically from a finite number of mock realisations. The resulting noise degrades inference and precludes it completely if there are fewer…

Estimating covariance matrices is a problem of fundamental importance in multivariate statistics. In practice it is increasingly frequent to work with data matrices $X$ of dimension $n\times p$, where $p$ and $n$ are both large. Results…

It is shown that the matrix models which give non-perturbative definitions of string and M theory may be interpreted as non-local hidden variables theories in which the quantum observables are the eigenvalues of the matrices while their…

We consider a $d$-dimensional continuous martingale $X(t)$ with quadratic variation matrix $\langle X\rangle_t=\int_0^t \Sigma(s)\,ds$ and develop tests for the rank of its spot covariance matrix $\Sigma(t)$, $t\in[0,1]$. The process $X$ is…

We consider the dynamics of bodies with "active" microstructure described by vector-valued phase fields. For waves with time-varying amplitude, the associated evolution equation involves a matrix that can be non-normal, depending on the…

A parameterization that is a modified version of a previous work is proposed for the returns and correlation matrix of financial time series and its properties are studied. This parameterization allows easy introduction of non-stationarity…

Advances in simultaneous recordings of large numbers of neurons have driven significant interest in the structure of neural population activity such as dimension. A key question is how these dynamic features arise mechanistically and their…

We describe a method to determine the eigenvalue density of empirical covariance matrix in the presence of correlations between samples. This is a straightforward generalization of the method developed earlier by the authors for…

Standard noise radars, as well as noise-type radars such as quantum two-mode squeezing radar, are characterized by a covariance matrix with a very specific structure. This matrix has four independent parameters: the amplitude of the…

This paper investigates the signal detection problem in colored Gaussian noise with an unknown covariance matrix. To be specific, we consider a sample deficient scenario in which the number of signal bearing samples ($n$) is strictly…

We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix…

Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…

Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…