Related papers: Wishart laws and variance function on homogeneous …
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 introduce a natural definition of Riesz measures and Wishart laws associated to an $\Omega$-positive (virtual) quadratic map, where $\Omega \subset \real^n$ is a regular open convex cone. We give a general formula for moments of the…
Let G = An be the graph corresponding to the graphical model of nearest neighbour interaction in a Gaussian character. We study Natural Exponential Families( NEF) ofWishart distributions on convex cones QG and PG, where PG is the cone of…
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…
In this paper, we give an explicitdescription of a class of positive measures on symmetric conesdefined by their Laplace transforms in the framework of the Rieszintegrals. This work is motivated by the importance of thesemeasures in…
In this paper we consider some hypothesis tests within a family of Wishart distributions, where both the sample space and the parameter space are symmetric cones. For such testing problems, we first derive the joint density of the ordered…
The aim of this paper is to study the mixture of the Riesz distribution on symmetric matrices with respect to the multivariate Poisson distribution. We show, in particular, that this distribution is related to the modified Bessel function…
In this paper, we introduce, for a multiplier $\chi$, a notion of generalized power function $x\mapsto \Delta_{\chi}(x),$ defined on the homogeneous cone ${\mathcal{P}}$ of a Vinberg algebra ${\mathcal{A}}$. We then extend to…
In this paper we consider two statistical hypotheses for the families of Wishart type distributions. These distributions are analogs of the Wishart distributions defined and parametrized over a Lorentz cone. We test these hypotheses by…
Let $W$ be a random positive definite symmetric matrix distributed according to a real Wishart distribution and let $W^{-1}=(W^{ij})_{i,j}$ be its inverse matrix. We compute general moments $\mathbb{E} [W^{k_1 k_2} W^{k_3 k_4} ...…
This paper deals with the Elliptical Wishart and Inverse Elliptical Wishart distributions, which play a major role when handling covariance matrices. Similarly to multivariate elliptical distributions, these form a large family of…
Random matrix theory has become a cornerstone in modern statistics and data science, providing fundamental tools for understanding high-dimensional covariance structures. Within this framework, the Wishart matrix plays a central role in…
Using Beck and Cohen's superstatistics, we introduce in a systematic way a family of generalised Wishart-Laguerre ensembles of random matrices with Dyson index $\beta$ = 1,2, and 4. The entries of the data matrix are Gaussian random…
We show that the derivative of the logarithm of the average characteristic polynomial of a diffusing Wishart matrix obeys an exact partial differential equation valid for an arbitrary value of N, the size of the matrix. In the large N…
We compute explicit bounds in the normal and chi-square approximations of multilinear homogenous sums (of arbitrary order) of general centered independent random variables with unit variance. In particular, we show that chaotic random…
We analyse the Cauchy problem on a characteristic cone, including its vertex, for the Einstein equations in arbitrary dimensions. We use a wave map gauge, solve the obtained constraints and show gauge conservation.
We use free probability to compute the limiting spectral properties of the harmonic mean of $n$ i.i.d. Wishart random matrices $\mathbf{W}_i$ whose limiting aspect ratio is $\gamma \in (0,1)$ when $\mathbb{E}[\mathbf{W}_i] = \mathbf{I}$. We…
This article derives several properties of the Riesz distributions, such as their corresponding Bartlett decompositions, the inverse Riesz distributions and the distribution of the generalised variance for real normed division algebras. In…
The Wishart probability distribution on symmetricmatrices has been initially defined by mean of the multivariateGaussian distribution as an of the chi-square distribution. A moregeneral definition is given using results for harmonic…
The normal-inverse-Wishart (NIW) distribution is commonly used as a prior distribution for the mean and covariance parameters of a multivariate normal distribution. The family of NIW distributions is also a minimal exponential family. In…