Related papers: Maximal Invariants For Lorentz Wishart Models
The joint distribution of two off-diagonal Wishart matrix elements was useful in recent work on geometric probability [Finch 2010]. Not finding such formulas in the literature, we report these here.
Covariance matrix estimation arises in multivariate problems including multivariate normal sampling models and regression models where random effects are jointly modeled, e.g. random-intercept, random-slope models. A Bayesian analysis of…
Based on a student research project this article gives a short review on Wishart processes. A Wishart procces is a matrix valued continuous time stochastic process with a marginal Wishart distribution. The Wishart distribution is a matrix…
The question of testing for equality in distribution between two linear models, each consisting of sums of distinct discrete independent random variables with unequal numbers of observations, has emerged from the biological research. In…
Vinberg cones and the ambient vector spaces are important in modern statistics of sparse models and of graphical models. The aim of this paper is to study eigenvalue distributions of Gaussian, Wigner and covariance matrices related to…
A new generator of univariate continuous distributions, with two additional parameters, called the Log-Lindley generated family is introduced. Some special distributions in the new family are presented. Some mathematical properties of the…
We consider a two-sample hypothesis testing problem, where the distributions are defined on the space of undirected graphs, and one has access to only one observation from each model. A motivating example for this problem is comparing the…
The Wishart distribution on an homogeneous cone is a generalization of the Riesz distribution on a symmetric cone which corresponds to a given graph. The paper extends to this distribution, the famous Olkin and Rubin characterization of the…
A Wishart matrix is said to be spiked when the underlying covariance matrix has a single eigenvalue $b$ different from unity. As $b$ increases through $b=2$, a gap forms from the largest eigenvalue to the rest of the spectrum, and with…
We establish connections between invariant theory and maximum likelihood estimation for discrete statistical models. We show that norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We…
This paper discusses the approximate distributions of eigenvalues of a singular Wishart matrix. We give the approximate joint density of eigenvalues by Laplace approximation for the hyper-geometric functions of matrix arguments.…
Modelling multivariate tail dependence is one of the key challenges in extreme-value theory. Multivariate extremes are usually characterized using parametric models, some of which have simpler submodels at the boundary of their parameter…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
Recently, the authors have proposed a new approach to the theory of random metrics, making an explicit link between probability measures on the space of metrics on a Kahler manifold and random matrix models. We consider simple examples of…
The prediction of the variance-covariance matrix of the multivariate normal distribution is important in the multivariate analysis. We investigated Bayesian predictive distributions for Wishart distributions under the Kullback-Leibler…
In the paper we present a characterization theorem of the Riesz measure and a Wishart exponential family on homogeneous cones through the invariance property of a natural exponential family under the action of the triangular group.
We propose a new class of semiparametric exponential family graphical models for the analysis of high dimensional mixed data. Different from the existing mixed graphical models, we allow the nodewise conditional distributions to be…
The skew-normal and the skew-$t$ distributions are parametric families which are currently under intense investigation since they provide a more flexible formulation compared to the classical normal and $t$ distributions by introducing a…
In this paper non-asymptotic exact rearrangement invariant norm estimates are derived for the maximum distribution of the family elements of some rearrangement invariant (r.i.) space over unbounded measure in the entropy terms and in the…
Recently the termed \emph{multimatrix variate distributions} were proposed in \citet{dgcl:24a} as an alternative for univariate and vector variate copulas. The distributions are based on sample probabilistic dependent elliptically countered…