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Geostatistical modeling for continuous point-referenced data has been extensively applied to neuroimaging because it produces efficient and valid statistical inference. However, diffusion tensor imaging (DTI), a neuroimaging characterizing…

This paper deals with the asymptotic distribution of Wishart matrix and its application to the estimation of the population matrix parameter when the population eigenvalues are block-wise infinitely dispersed. We show that the appropriately…

Statistics Theory · Mathematics 2008-04-06 Yo Sheena , Akimichi Takemura

In this study, we derive the exact distributions of eigenvalues of a singular Wishart matrix under an elliptical model. We define generalized heterogeneous hypergeometric functions with two matrix arguments and provide convergence…

Statistics Theory · Mathematics 2021-04-27 Aya Shinozaki , Koki Shimizu , Hiroki Hashiguchi

We study the behavior of a real $p$-dimensional Wishart random matrix with $n$ degrees of freedom when $n,p\rightarrow\infty$ but $p/n\rightarrow 0$. We establish the existence of phase transitions when $p$ grows at the order…

Probability · Mathematics 2017-05-11 Didier Chételat , Martin T. Wells

A complete characterization of Wishart distributions on the cones of positive semi-definite matrices is provided in terms of a description of their maximal parameter domain. This result is new in that also degenerate scale parameters are…

Probability · Mathematics 2010-09-21 Eberhard Mayerhofer

In this paper, we want to show the Restricted Wishart distribution is equivalent to the LKJ distribution, which is one way to specify a uniform distribution from the space of positive definite correlation matrices. Based on this theorem, we…

Computation · Statistics 2018-09-14 Zhenxun Wang , Yunan Wu , Haitao Chu

In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…

Probability · Mathematics 2018-06-22 Shane Barratt

This paper aims to examine the characteristics of the posterior distribution of covariance/precision matrices in a "large $p$, large $n$" scenario, where $p$ represents the number of variables and $n$ is the sample size. Our analysis…

Statistics Theory · Mathematics 2026-02-02 Partha Sarkar , Kshitij Khare , Malay Ghosh , Matt P. Wand

The correlated Wishart model provides a standard tool for the analysis of correlations in a rich variety of systems. Although much is known for complex correlation matrices, the empirically much more important real case still poses…

Mathematical Physics · Physics 2015-02-13 Tim Wirtz , Mario Kieburg , Thomas Guhr

Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these…

Statistics Theory · Mathematics 2020-05-15 Sharon X. Lee , Geoffrey J. McLachlan

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…

Logic · Mathematics 2007-05-23 Joy Jacob , Sebastian George , A M Mathai

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…

Statistics Theory · Mathematics 2012-01-04 Emanuel Ben-David

Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex…

Mathematical Physics · Physics 2013-10-21 Tim Wirtz , Thomas Guhr

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…

Statistics Theory · Mathematics 2009-07-07 Jose A. Diaz-Garcia , Ramon Gutiérrez Jáimez

Gaussian covariance graph models encode marginal independence among the components of a multivariate random vector by means of a graph $G$. These models are distinctly different from the traditional concentration graph models (often also…

Statistics Theory · Mathematics 2011-03-10 Kshitij Khare , Bala Rajaratnam

We develop a nonparametric two-sample test for distributions supported on the cone of symmetric positive definite matrices. The procedure relies on the Wishart kernel density estimator (KDE) introduced by Belzile et al. (2025), whose…

Statistics Theory · Mathematics 2026-03-17 Frédéric Ouimet

Hilbert-Schmidt distance is one of the prominent distance measures in quantum information theory which finds applications in diverse problems, such as construction of entanglement witnesses, quantum algorithms in machine learning, and…

Quantum Physics · Physics 2020-08-13 Santosh Kumar

The scaled complex Wishart distribution is a widely used model for multilook full polarimetric SAR data whose adequacy has been attested in the literature. Classification, segmentation, and image analysis techniques which depend on this…

Machine Learning · Statistics 2023-07-19 Alejandro C. Frery , Abraão D. C. Nascimento , Renato J. Cintra

We define an indefinite Wishart matrix as a matrix of the form A=W^{T}W\Sigma, where \Sigma is an indefinite diagonal matrix and W is a matrix of independent standard normals. We focus on the case where W is L by 2 which has engineering…

Statistics Theory · Mathematics 2015-12-21 Ramis Movassagh , Alan Edelman

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.…

Statistics Theory · Mathematics 2023-06-09 Koki Shimizu , Hiroki Hashiguchi