相关论文: Matrix Moments in a Real, Doubly Correlated Algebr…

We introduce a new method for estimating the covariance matrix for the galaxy correlation function in surveys of large-scale structure. Our method combines simple theoretical results with a realistic characterization of the survey to…

The aim of this paper is to present a systematic method for computing moments of matrix elements taken from circular orthogonal ensembles (COE). The formula is given as a sum of Weingarten functions for orthogonal groups but the technique…

We provide a complete description of possible covariance matrices consistent with a Gaussian latent tree model for any tree. We then present techniques for utilising these constraints to assess whether observed data is compatible with that…

Mixed-moment models, introduced before for one space dimension, are a modification of the method of moments applied to a (linear) kinetic equation, by choosing mixtures of different partial moments. They are well-suited to handle such…

This paper develops an efficient Monte Carlo method to estimate the tail probabilities of the ratio of the largest eigenvalue to the trace of the Wishart matrix, which plays an important role in multivariate data analysis. The estimator is…

Although stochastic volatility and GARCH (generalized autoregressive conditional heteroscedasticity) models have successfully described the volatility dynamics of univariate asset returns, extending them to the multivariate models with…

In this paper we study linear non-Gaussian graphical models from the perspective of algebraic statistics. These are acyclic causal models in which each variable is a linear combination of its direct causes and independent noise. The…

Precision matrix, which is the inverse of covariance matrix, plays an important role in statistics, as it captures the partial correlation between variables. Testing the equality of two precision matrices in high dimensional setting is a…

Consider a high-dimensional Wishart matrix $\bd{W}=\bd{X}^T\bd{X}$ where the entries of $\bd{X}$ are i.i.d. random variables with mean zero, variance one, and a finite fourth moment $\eta$. Motivated by problems in signal processing and…

Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive…

The iterative algorithm recently proposed by Waxman for solving eigenvalue problems, which relies on the method of moments, has been modified to improve its convergence considerably without sacrificing its benefits or elegance. The…

We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance…

In a brief review, we discuss interrelations between arbitrary solutions of the loop equations that describe Hermitean one-matrix model and particular (multi-cut) solutions that describe concrete matrix integrals. These latter ones enjoy a…

Correlated data are ubiquitous in today's data-driven society. While regression models for analyzing means and variances of responses of interest are relatively well-developed, the development of these models for analyzing the correlations…

In this paper, we develop a novel approach to the Weingarten calculus by employing the notion of virtual isometries. Traditionally, Weingarten calculus provides explicit formulas for integrating polynomial functions over compact matrix…

A Bayesian procedure is developed for multivariate stochastic volatility, using state space models. An autoregressive model for the log-returns is employed. We generalize the inverted Wishart distribution to allow for different correlation…

Properties of universality have essential relevance for the theory of random matrices usually called the Wigner ensemble. The issue was analysed up to recent years with detailed and relevant results. We present a slightly different view and…

Motivated by recent results in random matrix theory we will study the distributions arising from products of complex Gaussian random matrices and truncations of Haar distributed unitary matrices. We introduce an appropriately general class…

The joint moments of the derivatives of the characteristic polynomial of a random unitary matrix, and also a variant of the characteristic polynomial that is real on the unit circle, in the large matrix size limit, have been studied…

Modeling complex systems, like neural networks, simple liquids or flocks of birds, often works in reverse to textbook approaches: given data for which averages and correlations are known, we try to find the parameters of a given model…